Ezra's right that tax brackets don't make taxes difficult, the deductions do, but it's precisely the reason why the AMT is so unpopular - one doesn't just glance at your annual income and say "oops, I guess I'm going to pay at the 28% rate this year." One has to go through the process of accounting for and taking all of the deductions they tell you that you're entitled to take, and then right at the last minute the AMT monster says "psyche!" and takes them back.
So, no, the AMT doesn't simplify anything about doing taxes. It makes them more complicated as it's no longer transparent what your deductions can be.