Well, let's look at what the report actually says,
"The United States scores poorly largely because it maintains the highest corporate tax rate in the developed world at 39.1 percent and is one of the six remaining countries in the OECD with a worldwide system of taxation," the Tax Foundation said. "Its poorly structured property, individual, and capital gains and dividends taxes also contribute to the low ranking."
"No longer can a country tax business investment and activity at a high rate without adversely affecting its economic performance," a co-author of the report, Kyle Pomerleau, said in a statement. "In recent years, many countries have recognized this fact and have moved to reform their tax codes to be more competitive. However, others have failed to do so and are falling behind the global movement."
So what that report is complaining about is primarily a high nominal rate (39%) on corporate income that is charged globally. The effective rate is lower, around 27%. To get that lower effective rate, they implement a lot of deductions. So roughly a third of income is exempt from taxation for one reason or another.
They also charge corporations tax on all income earned globally. Because other countries mostly charge tax just on income earned in their own territory. This produces a situation where companies are incented to locate their headquarters outside the US but do business in the US. Because that combination avoids the global and territorial taxes. And companies are incented against locating their headquarters in the US and doing business outside the US, because then they pay both global and territorial taxes. Companies that have to do that often leave their profits in their overseas subsidiaries so as to avoid the global tax on returning income.
Property taxes are local (county, school district, and municipality) taxes. The Tax Foundation doesn't like them because rich people pay a lot.
The point being that those issues have nothing to do with choosing who pays individual income tax. They are complaining a lot about how business taxes are structured rather than personal taxes.
The Quora post is focusing on something different. Because of the way that the US tax code developed, they repeatedly found ways that the tax code was unfair and charged people who had no excess income to pay the taxes. So they added exceptions. Then people that did have money to pay the taxes would find new ways to use the exceptions. So the government would make a new rule to catch those people.
Take the deduction on state and local taxes for example. Typical working class people can't take this. Even if they have enough income to pay income taxes, they don't pay enough state and local taxes to be worth replacing the standard deduction with itemized deductions. Most middle class people who take this deduction combine it with the deduction for mortgage interest.
The simple fix for all this would be to get rid of the deductions on mortgage interest and state and local taxes and increase the standard deduction. But of course that is unpopular with people who took the deductions in the past, who currently take the deductions, or who think they might take the deductions in the future. That is so even if they would actually be better off with the higher standard deduction.
What they actually did was to create something called the Alternative Minimum Tax (AMT). The AMT says that even after taking deductions, higher income people must still pay a certain amount of tax on employment income. But the AMT rate is still below the top marginal rate. So there is a lot of incentive to pay just the AMT rate, making a mockery of the top rate. And the AMT rate doesn't apply to capital income (capital gains, dividends, etc.).
There is also a problem in that there is a business in preparing taxes. While full time participants may only be about 40,000, over a million people do paid tax preparation during tax season. Those people and various software companies with tax preparation software have an incentive to keep taxes complicated. So they lobby against any changes to simplify the tax code. Not only do they lobby politicians, but they also demonize changes with the general public. For example, they oppose eliminating the mortgage interest deduction.
The problem is that the mortgage interest deduction sounds great on its face. Encourages home ownership! Gives a break to families struggling to afford their house! But in practice, the actual savings for those kinds of families are small. The people who really benefit are those at the upper end of the deduction. And the truth is that someone who can get a $500,000 mortgage is not that poor. So a bad policy continues because it sounds much better than it actually is.
This is less of an issue with business taxes, as businesses expect to pay accountants regardless. There isn't the same pressure to keep the taxes complicated to keep business accountants employed.
That is a downside of charging taxes to individuals. The paid tax preparer lobby then has an incentive to keep taxes complicated.
There is an upside though. If the businesses are making tax payments for employees who actually owe the tax, then that gives two groups who are responsible for reporting income and auditors can catch either of them not reporting. It's the same principle as Value-Added Tax (VAT). Because the seller remits the tax but it is the buyer who pays it, the seller has less incentive to avoid paying the tax. And the buyer actively wants proof of paying the tax, as they can deduct taxes paid against their own tax payments.
In theory, charging the tax just once would be simpler. In practice though, people still have to file the paperwork anyway. Because they have to explain why they did not charge the tax. Paying the tax at each step is about the same work and makes it so that there is one party that wants to report it.
Moving to an income tax system where individuals are responsible, but businesses actually handle most of the payments works the same way. The employees want credit for the taxes being paid. If the employers just pocket the taxes, then they can't deduct the employee's wages or salary from the business income taxes. And they risk getting caught if someone notices that the employee has money but no income.
If I were creating a system from scratch, I'm not sure that's how I'd do it. Rather than making employers remit the tax, I'd have banks do it. Because the truth is that they are in a better position to see all the income than employers. But there are reasons to support an income tax (owed by individuals) over a payroll tax (paid by businesses).
Another reason is that individuals pay taxes on things other than their employment compensation. Capital gains, dividends, interest, business income, etc. It's not clear to me how those get charged in your system, so I won't comment on specifics. (That's not a question--this is already at the broad end of the question spectrum. It would probably be better to ask about that kind of stuff in a separate question if you're still curious.)