The question is titled:
Why is it a bad idea to hire a hitman [to kill corrupt] politicians?
Well, from a moral standpoint, it's wrong. It depends on your yardstick for corruption, but let's say as you imply it's some run of the mill embezzling/defruading the state.
You've implied a benchmark of:
whenever politicians became too shameless in their corruption schemes,
..implying financial misconduct.
That's an abuse of power and generally considering to be "wrong" (in the ethical sense). However, if we look at this on the basis of first principles: If I steal ten dollars from you, and you then come and kill me (hiring someone is more or the less ethically the same thing), who's committed the greater wrong, me or you?
I think you'd be hard pressed to find someonewho argues that stealing money is ethically worse than killing someone - it's disproportionate. The key attribute of retributive jsutice is that it is proportionate. To quote Wikipedia:
Retributive justice is a theory of justice that holds that the best
response to a crime is a punishment proportional to the offense,
inflicted because the offender deserves the punishment. Prevention of
future crimes (deterrence) or rehabilitation of the offender are not
considered in determining such punishments. The theory holds that when
an offender breaks the law, justice requires that he or she suffer in
return. Retribution is different from revenge because retributive
justice is directed only at wrongs, has inherent limits, is not
personal and involves no pleasure at the suffering of others and
employs procedural standards. Classical texts advocating the
retributive view include De Legibus (1st century BC), Kant's Science
of Right (1790), and Hegel's Philosophy of Right (1821).
From an ethical standpoint, it seems evident that hiring a hitman to kill a corrupt politician is both unjust and unethical - to a certain degree. There's also an inherent problem with your criterion:
too shameless in their corruption schemes
Your benchmark here is how visible this corruption is, or more precisely, how corrupt the individual is perceived to be. This is problematic. Let's discuss the ethical reasons first, then move on to why pragmatically this is even worse.
So the next question is: How shameless is "too shameless" ? What amount of money or kind of corruption schemes are objectively worth "sending a message over"? If, as I think you will agree, stealing ten dollars from the government not worth hiring a hitman over, what figure is ? Ten thousand dollars, one hundred thousand? What price do you put on a human life? Who gets to deem that the politician is too shameless?
The problem with this unilateral approach is that a lot of people might not agree with your methods, or your reasoning. Look at Lee Harvey Oswald, John Wilkes Booth or Mark David Chapman: Complete nutters the lot of them. How do you verify when you embark on this course of action that you yourself aren't just, yourself, a complete nutter? Unlike a functioning judicial process, there's no due process or checks and balances. Looking at today's political climate, there are probably a lot of people who would feel justified in taking that action into their own hands, even though, their criterion for action might not meet the same standards as yours.
Whilst I am no Trump fan, I certainly don't believe he should be assassinated. There are plenty of people in the U.S who do and I am certainly not comfortable with their ethical standards because if those same principles were applied, they would feel justified in killing a lot of people I would consider innocent, or at least not worthy of summary extrajudicial execution.
Can you imagine what it would be like if every SJW, right wing blogger and Youtube commenter felt they were justified in taking the lives of people who had transgressed their imaginary rulebook?
We need to also ask whilst on the topic of personal culpability, what is a politician? At the most abstract, I submit it's somebody who influences or attempts to influence the body politic. So by killing someone you perceive to be corrupt, or a lizard person, or whatever, you are in fact attempting to influence the political process. So if you hire a hitman to kill whoever, isn't somebody else justified in viewing you as corrupt and hiring a hitman to take you out?
These are just some quick moral arguments against it off the top off my head. There's a far greater problem with this notion. It doesn't really work.
First of all, let's examine your proposition:
someone hired a hitman that eliminates a few important figures,
basically sending a message that most of the people are thinking: "We
can see what you're doing and we won't just stay and do nothing"? In
my very naive opinion, this will send a warning message to any future
person occupying that role that they shouldn't fall into corruption
schemes or at least not as much.
Well, for starters, I don't think the politician in question will be falling into any corruption schemes anymore, assuming that the hitman is successful. So what message are you really sending? And to whom? The guy's dead.
So how are you getting your message across? No doubt if the politician is visibly corrupt enough, people might suspect it had something to do with it but there's no clear cut guarantee. Declaring some manifesto alongside it only increases your risk of getting caught.
Aside from your hitman probably having something to say about that; what guarantee do you have that either this corrupt cabal or the general populace is going to take you seriously? It's a nice daydream, but I don't think it really works out that way in practice.
There's another fatal flaw with your plan: Darwinism.
You see, by your stated criterion, you're only targeting the most visibly corrupt politicians. Let's assume you have a lot of money and a really good hitman. What happens in the long run? You don't kill all the corrupt politicians, you just kill the visible, and, by extension, the inept ones. That just ends up leaving the ones who excel at being corrupt. This leaves you worse off than where you started. This happens a lot in nature.
For example, we've possessed the genetic weaponry necessary to wipe out the malarial mosquito for sometime. The reason why we haven't done it, is that even though malaria kills a lot of people is that we don't know exactly what else it kills and what effects might result.
We might inadvertantly lift the lid on another disease that's even worse. One of these politicians might be corrupt but be keeping someone even worse from rising up the food-chain.
You see, for politicians to become so shameless unaccountable to their electorate, it doesn't just imply that they themselves have taken advantage of the government. What it usually means is that the institutions of government - the complex systems and ecosystems of government and governance have themselves broken down. It's quite easy for people to point to a divisive figure like say, Donald Trump, and say "It's all his fault" but the reality is that these people are the symptoms of the problem, not the cause.
The United States has had real trouble just functioning for a long time, and its democratic institutions are in many ways fundamentally broken. The causes of this are legion, but can basically be summed up with their culture and history has directly determined the outcome they have right now. Likewise, the failure of institutions and democracy in Hungary or Poland or Bulgaria (or wherever you are) aren't the result of just one person but a systemic failure. You can't cure this with a bullet - people have tried.
This leads to my last point: Unintended consequences.
We don't know what forces might be unleashed by a single assassination. Look at Archduke Ferdinand. He was killed because he was a symbol of the Austro-Hungarian domination of the Balkans. Princip believed that by assassinating him he was furthering the course of Serbian freedom. Ironically Ferdinand was a reformer, and they had a better chance under Ferdinand.
What happened instead is that the vast machinery of Europe, having almost stepped back from the brink of war, was thrown into four years of wanton and unnecessary bloodshed. The Serbian state was nearly utterly destroyed. It set the preconditions of the Second World War which was the most destructive war in history. The consequences of that single action set of a chain of events that led to the deaths of up to 100 million people.
Now maybe assassinating Viktor Orban or Justin Trudeau or whoever wouldn't set off such a conflagration, but here's the thing: you just don't know. If you paid someone to pull the trigger, all that blood is essentially on your hands.
I could go on to list all the times this hasn't worked or how internal power struggles in crumbling democracies often fail to deliver an improvement in living conditions and civil rights for the people.
The Arab Spring is a rather depressing reminder of how even well intentioned grassroots attempts at overthrowing tyranny can lead to both its entrenchment and expansion - look at Eygypt, Syria and Libya.
I think you'll also find that decapitating the leadership might effectively, most systems are somewhat resilient to it. We can look the Taliban, Al-Qaeda for examples on how despite numerous attacks/assassinations of leaders, they remain just as capable of carrying on fighting as long as their support networks are in place.
So going back to incentives. I mentioned before that in the event you described wasn't worth killing someone over. So when is it?
Let's consider briefly the Trolley Dilemma.
You see a runaway trolley moving toward five tied-up (or otherwise
incapacitated) people lying on the tracks. You are standing next to a
lever that controls a switch. If you pull the lever, the trolley will
be redirected onto a side track, and the five people on the main track
will be saved. However, there is a single person lying on the side
track. You have two options:
Do nothing and allow the trolley to kill the five people on the main
Pull the lever, diverting the trolley onto the side track where
it will kill one person.
Which is the more ethical option?
Another commenter brought up the example of how members of the German military tried to assassinate Hitler (I believe they tried a couple of times) and instigate a coup.
Intriguingly, someone else brought up Duterte.
There's only an ethical and pragmatic case to kill a politician where there is a clear threat to the lives of people under the rule of that person - where you can make a clear case that intervening would stop this person killing or enacting policies that would directly and explicitly result in killing innocent people. Killing Hitler might have shortened the Second World War and prevented part of the Holocaust.
In the case of Duterte, who has openly advocated and directly enabled the extrajudicial killings of tens of thousands of people, there is in fact an ethical, and perhaps, pragmatic case to intervene. This is clear and distinct from policies by national leaders who have decided to go to war in what they perceive to be the national interest, such as Russia or the United States.
These aren't ideal either, but quite distinct from using murder as an instrument of social policy. I submit that hiring a hitman to kill a single person differs only in magnitude to these crimes however, not only is it inethical in the scenario you are talking about, but from a practical standpoint, it's likely to be ineffective - and therefore even more unforgivable.
The best way to fight corruption is to build strong and empower strong democratic institutions with respect for the rule of law. This is probably cold comfort to someone living in Eastern Europe where corruption and illiberalism has been the norm for a very long time.
N.B. Please forgive what is a rather rough draft as I am procrastinating from programming at 4am. That said, probably a bad idea to kill politicians.