The current state of the world is such that the "communist" attitude is frowned upon, whereas alternatives like "capitalism" and "meritocracy" are preferred.
For example when we hitch a flight on an aircraft, no one would think that it's a problem when someone who can afford to (willing to) pay more receives a premium-class seat, as opposed to someone who couldn't.
The logical inference seems to be that citizens who donate* more to public works should deserve more votes, up to a limit per head. However, in many regions we have the system of "one man one vote" whereby each qualified citizen is entitled to one vote, no more, no less. Yet, that seems to directly contradict with the preferred "capitalism" / "meritocracy" attitude.
Why is "one man one vote" used throughout the world despite contradicting "capitalism" which seems to be preferred?
* Just assume that we have this country whereby public works are funded not by tax, but by crowdfunding.
It is a common misconception that democracy and capitalism are part and parcel with each other and inseparable.
Democracy is a political system whereby rule is by the people - while Capitalism is an economic system whereby the free market is well-regarded (by and large).
Of course both of these have manifested in a number of variations and there exist plenty of more variants that may or may not have been tried.
Monarchy and Democracy? You have the United Kingdom.
Socialism and Democracy? You have a number of EU states - Including Malta.
Capitalism and Democracy? You have the United States.
A lot could be said about existing systems - and even more could be said about systems that 'could' exist - but let it suffice to say that Capitalism and Democracy do not 'have' to co-exist within any given economy.
Even in the above examples (not indicated as Capitalist) a significant degree of Capitalism is alive and well.
As such, since the comparison is not like with like, your original question is a little similar to "If law enforcement promotion procedures are so unfair then why are schools being funded?". Each of the elements can exist without the other.
Democracy and Meritocracy are more able to be validly compared as a political system.
Socialism and Capitalism are likewise more valid for comparison purposes - both economic systems. Alternatively Communism if you find the comparison prospect more interesting.
A plutocracy is a form of oligarchy, where society is governed by the small minority of the wealthiest citizens. A meritocracy can also be considered an oligarchy, but is based on the notion that power should be vested in individuals almost exclusively based on ability and talent. Wealth by no means implies ability or talent.
Anyway, the current Western form of government is plutocracy masquerading as democracy. The reason it is masquerading as democracy, should be obvious: it creates the illusion that the masses have political power, effectively discouraging them from engaging in violent revolts.
As long as the great masses believe that real "change they can believe in" can come from coloring a dot every couple of years, they are not inclined to conspire against the oligarchy and start a violent revolution. As long as you believe that change can come from voting for whatever puppet of the oligarchy you favor, you will keep believing in "democracy" and reject the very notion that revolution might be necessary.
Other answers emphasize on the fact that capitalism and democracy are two disctinct concepts. That is correct. But I'll go further : There is a contradiction between capitalism and democracy. You give examples that make it seem like most of these contradictions have been overcome nowadays, but it wasn't always like that, and it still is not in some aspects of our society:
Think of the early days of capitalism (18th and 19th century): in many countries, universal suffrage did not exist. The right of voting was restricted to "appointed electors" (which is still the case in the electoral college in the US and many other institutions), which were often local men of influence, which often translates to men of power. Back then, that meant wealthy bourgeois. In other words : the richer you were/are, the more you could vote, in more institutions. It was/is not "one man one vote".
Still nowadays, in some countries, the main goal of unionists is to make it possible for the workers to vote on the decisions within the company. You might consider this outside of the scope of democracy, but that is not the opinion of many socialists or unionists, who think that workplaces are an extension of the citizenship and should be subjected to the same rules as your regular democracy. And, in the company, guess what? The shareholder holding the most shares has much more decision power -- the votes of the board count more than others. In other words : it's not "one man one vote". It's "one dollar one vote".
These are two examples where the "one man one vote" principled is/was overlooked in capitalistic democracies.
Capitalism, Democracy, Meritocracy, and Liberalism are four very different concepts, so we need to talk some definitions.
Democracy is the idea that a body of the population may vote on the direction of government to some degree. Not all Democracies are Liberal Democracies (For example, Iraq under Saddam Hussein was an Illiberal Democracy. The people could vote if they wanted Saddam to continue to be President. If you voted no however... well, let's just say your vote doesn't count anymore...).
Capitalism is the belief in a competitive market and all that fun stuff. It's directly opposed by Socialism, which is state controlled markets and there is no competition. Capitalists often feel government is the worst management system for a business.
Meritocracy is the concept that a particularity job or duty should to to the best candidate to perform that task, and that should be the only metric by which we consider candidates for a position.
Liberalism is an ideology that basically argues that the government's most important job is the protection of the individual and his or her rights, but the government should not interfere with the individual's rights to Life, Liberty, and Property (Thomas Jefferson changed this to Life, Liberty, and the Pursuit of Happiness because Jefferson was a epicurean, which is someone who believe that one should be free to pursue that which makes him/her happy.). Liberalism is basically to Communism what Capitalism is to Socialism, that is, Capitalism is a core tenant of Liberalism in Economics but not everything Liberalism is about. At the end of the day, most Americans are Liberals (including the "Conservatives... they actually tend to be closer to European Liberal parties than European Conservative Parties... America can be weird with it's political terminology).
Now, all this is to say that not everything is inherently "anti-communist". Just Capitalism and Liberalism. Both Liberalism and Communism are amiacable to Democracy, just different forms of it. Actually, Liberalism originally was sort of quiet on the organization of government. John Locke actually favored a Liberal Monarchy as his structure system. It was the United States of America that really married the idea of Liberalism with Democracy. Americans loved them some Lockian Liberalism but really had a historical love of Greco-Roman Government structures (Democracy from Greece, Republicanism from the Romans... again with the weird terminology... most Americans use "Republic" as a substitution for Representative Democracies, and not "any government without a king".).
Finally, Capitalism and Communism both like Meritocracy, but use it differently. The USSR tended to place people in jobs that they were going to be the best at... Capitalism will generally hire anyone for a basic job and "let the cream rise to the top"... You may start all McDonald's workers at the same salery, but the ones who are good at making burgers are going to get promoted. Jobs that require higher demands are given to people who can prove they can perform the best at this task... everyone is a Meritocrat when it comes to hiring a Nuclear Safety Inspector (even Mr. Burns. Remember his original reason to hire Homer Simpson: Homer was really good at finding potentially dangerous situations, pointing them out, and getting people to pay attention... if you think about it...).
It's not that most of the ideologies are wrong, but rather, the U.S. in particular and much of Western Europe in general favored Liberalism as a political ideology.
There's no correlation between citizenship and wealth. A nation has citizens. Each citizen has a single vote. The reason why you can't have votes that correlate to wealth or public contribution is that, what markets value is not the same as what society values and by linking physical wealth to ones impact on the democratic process you in essence tether policy to wealth.
What that tethering does, is value the stockholders in democracy, not the stakeholders. Which is very bad. Government and Society must always try dull or alleviate the side effects of whatever economic system is at work in the society. There are many mindsets that attempt to solve these problems in different ways. But in short, allowing wealth to decide the value of a vote, is Oligarchy. Rule of the few, with the facade of equity.
It would simply destabilize society and you'd likely have a revolution. The idea of one person one vote, binds our fate together as citizens. It hold us all accountable for outcomes. The moment some other variable starts putting its finger on the scale, the whole thing starts to collapse because people then feel helpless. They no longer have the ability to self-determination. They would in short, feel unrepresented in society. And seeing as even the wealthy need non-rich to keep the rest of society running, it's in their self interest too to keep society stable. The lack of feeling represented in a society is in essence, a reflection of how legitimate we feel our government is.
You contribute to the public good because the stability that wealth into the government provides; allows wealth to be both protected and grow. Because governments protect wealth any change to destabilize the government would be a risk to anyone who has a material wealth. That cohesion is important. The moment a society feels that government isn't legitimate, the entire society is poorer for it.
TLDR: It's about legitimacy. No legitimacy, no stability. No stability, no state. No state, no prosperity.
As I understand it, it's all about history. Speaking from the perspective of USA, capitalism has always been the economic situation. However, the US has never been a real democracy. We are run by the rich, and always have been. At first, only land-owning males could vote; nowadays campaign contributions, lobbyists, etc. make the government owned by corporations.
The reason why the government claims that we're a democracy is because we don't want a French Revolution. Oh, and it keeps people patriotic enough to die overseas so that we can have cheaper oil.
The reason why we don't like the idea of socialism and communism is because of the cold war. There were actually a lot of communists in the US after the Great Depression (can't imagine why), but then communism became a dirty word and if you happened to work in government, you were fired.
The simplest answer is that in democracy, the benefit of majority rules.
Many aspect of capitalism benefit majority.
If Burger King have to compete with Mc Donald, there are far more people benefited by their competition. On the other hand, trade restrictions and monopoly hurt the majority of people.
Hence, in most cases, again and again, majority of voters vote in favor of rules that are aligned with capitalism.
It's natural that majority of people, who are customers and workers, vote for capitalism.
In area where the number of people that are made worse off are larger than the number of people that are made better off, the people do not vote in favor of capitalism.
A way to test this theory is to see whether democratic country is still "capitalistic" if competition affect the majority of people.
For example, do we have free market on labor market and sex market? In those cases, the number of people that will be made worse off under capitalism start becoming significant. Hence, we do not have free market on labor market and sex market.
So, capitalism govern which cell phone. Capitalism do not govern how many wives you can have in democratic countries.
Capitalism reduces incentive to be dictators
Another reason I can think off is that under capitalism you can get rich anyway normally. Hence, you do not need to be dictators to be rich. This reduces probability that a country would end up being lead by a dictator.
Basically, in free market economy, most people have a way to achieve success. Hence, they do not fight toe and nails to have more power over others.
In the absence of capitalism, the way to be richer than others is to be king. That is, one guy got all the vote.
With capitalism, I can be Bill Gates. A peasant like Bill Gates can be rich. So I don't bother if power is "socialized" I have other way to be "ubber alles". Namely getting rich productively.
This is probably why socialist countries end up being authoritarian. To get rich in socialist country you need to be the de facto king. You can't get rich normally. And that's what success no matter what minded people do. They become dictators, corrupt officials, etc.
Democracy can lead to socialism
I see an opposite factor where democracy may undermine capitalism and people that want meritocracy may want to avoid it.
In democracy, wealth tend to get redistributed to voters. However, these wealth redistribution is actually not very efficient. If the market decides a start up founder should be 10000 times richer than a blue collar workers, then that is simply what's "optimum". Under democracy, some of the money would go to the more numerous blue collar workers to get their votes.
So a way a country can create wealth more quickly is to keep workers out of power. Hence, a country can get very wealthy without having to raise minimum wage.
And that's what's happening in China.
What's ironic, is that China, being a communist country, is more capitalistic and meritocratic than a democracy. If it were a democracy, then the wealth disparity will be less.