Simplifying the tax code will require removing special exemptions for certain interest groups. This is often rephrased as "raising the taxes on [group]" which gets a lot of pushback. For example, raising the taxes on teachers, native americans, certain small businesses, public servants, antarctica scientists, students at for-profits, etc. It's hard to fight against that message.
One proposal here is to eliminate the ordinary income tax, and keep only the AMT, which is much simpler. The political advantage is that nobody gets a tax increase, and nobody's taxes get harder. And the revenue loss is surprisingly small - estimated at $63 billion annually in 2010 (though perhaps higher now due to the lower SALT limits).
I am in camp-AMT-only and it seems like both parties could get on board.
