I think part of the reason people want “the rich” to pay more taxes is that the Ebenezer Scrooges of the world are so good at finding ways out of paying their fair share of the tax burden. If we just eliminated a lot of the loopholes and tax breaks, and charged a simple progressive tax across the board, it’d accomplish a couple of big goals:
1) Easier for individual Americans to file their own taxes.
2) Easier for government to hold individuals responsible for failure to pay.
3) Easier to ensure that everyone pays a fair amount, making tax breaks a true incentive rather than “just another loophole”.