James Stewart points out that the merely rich (who rely more on labor income) often end up paying a much higher tax rate than the super rich (who rely more on capital income). And the AMT, which was meant to fix this problem, does not.
It seems like a political no-brainer that the top 0.01% should pay a higher tax rate than the top 1%. Since they do not, the question then is why? Do they have more political access? Does Congress identify with the top 0.01%? There must be some connection.