I understand the purpose.
However, in a democracy where everyone can vote... you run into problems when taxation does not equal representation.
By having different tax rates for people that are wealthier... while at the same time not increasing their influence over government relatively... you create a situation where one faction can vote themselves something at someone else's expense and the system is unable to balance the interests.
That is the problem with progressive taxes. They do not come with corresponding influence for those that pay more.
If you are prepared to reduce the influence of those that pay less or increase the influence of those that pay more... then go for it. Otherwise, progressive taxes should be avoided.
Further note that I am referring to tax RATES. If I make a million dollars and I pay a rate of 10 percent then I'm going to pay a lot more money then someone that makes 1000 dollars and also pays 10 percent. However, note that the rates are the same. That is fine. The problem comes about when the guy making a million pays a rate of 70 percent and the guy making a 1000 pays a rate of negative 900 percent. And yet they both have the same influence over the political process when they go to the ballot box.
Now you might say the rich man might get more influence buy donating to politicians. This is true. However that comes as an expense ON TOP of his taxes. He doesn't just get that. He has to pay even more money just to get the influence he should have gotten simply by paying those progressive taxes.
Now look, I don't want rich people to have that much influence. I like the idea of one person one vote.
But the price of that is that we all have to pay the same rate. Another option might be limiting what people on subsidies can vote on. I know... it sounds terrible but it might be fair. If society is basically feeding you, housing you, etc... then do you have a right to tell the rest of society how it must do it? I don't see that you do. At that point you are a dependent of the state not unlike being a child taken care of by a parent. And children don't get to vote.