Many politicians also feel that a flat tax rate isn't sufficiently progressive; that only by taxing higher incomes at higher percentages than lower incomes is it "truly" progressive.

OTOH, many politicians do want to see the tax code vastly simplified- they want the sort of system where you could fill out your taxes on a form small enough to fit on the back of a post card.

Everyone has their favorite thing that they want exempted (farms, capital investments, social security / welfare disbursements, medical expenses, school expenses, mortgage interest, rent, etc), and there are millions who would be put out of work by it- accountants, tax preparers, much of the IRS would be redundant, etc.

All of these competing interests keep us where we are. Blaming it on the "rich people" is lacking in any sort of honest intellectual rigor.