Even if we assume that your premise is correct that the rich deserve to pay more, there are 2nd order effects to consider. The rich may respond to tax hikes by raising the price of their goods and services, by moving their taxable income/wealth offshore, or by producing less/retiring.

Here's an interesting thought experiment: Temporarily imagine our economy as a barter exchange between the rich and the poor. If the exchange rate between goods and services provided by the rich and goods and services provided by the poor remains constant, then no tax policy could ever possibly change the income distribution.