"It is not "fair" that some people pay no income tax and others pay up to 30% or more."
If that is the case, then perhaps all such taxation should be abolished. No tax on income.
Tax purely on purchase.
With modern technology, one's purchasing power could be en-registered on her/his payment card. The 'sales tax' would be in proportion. That way, it would be simple, immediate and progressive at the same time.
As you note, even sales tax can be argued to be 'progressive'. The only truly 'fair' tax, if we're aiming at each of us taking equal responsibility for supporting the government, would be a head tax where we all pay the same amount every year. Pretty much every other taxing scheme is going to take more from some, and that will almost always - for pragmatic reasons if nothing else - be based on ability to pay.
That's why I'm not that emphatic about the 'flatness' aspect of the proposal. In my view, the elimination of incentives and loopholes would do much more to constrain the taxation power and return a sense of fairness to the tax code.
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