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A simple uncheatable tax doesn't need to be flat.
Years ago I came up with an algorithmic progressive tax that tracks the income distribution curve.
Using the 2011 numbers I could get 1% increments for. With a top tax rate of 40%, the bottom ~85% of people had a tax rate below 5%, and the budget that year would still balance.
And being a fixed algorythm, it's completely closed to manipulation. Unless you lie about your income, but that's already a felony.
But what if you creatively identify your income? And then get a bonus of a bunch of stocks, which you then leverage with a bank loan?..... oh right, that's how a lot of them do it already.
That would be the lying part.
Eventually those shares would be sold, or inherited. That income would be taxed at whatever the algorithm dictates.
So, we're back to playing the "algorithm" with what defines income, and what defines inherence, sale, etc of shares.
Sounds like essentially what we've got, just with the handwaving of "algorithm" instead.
It eliminates the picking and choosing of tax brackets. What you're talking about is making definitions. There is no way to mathematically fix that.