I mean, great, but the GOP will never let this happen. the Senate will kill this before it even gets to committee, let alone a floor vote.
For instance, if your capital gains tracked inflation precisely it seems fundamentally unfair to tax a percentage of the gains, as the person has not really "gained" in real terms.
Living expenses do not simply increase as a linear function of income or wealth. They increase, sure, but there's an effective upper bound. Jeff Bezos does not need to buy 10,000 times more food (or food 10,000 times more expensive) than someone making minimum wage.
Thus, the statement that "in a flat system, the rich contribute more," while trivially true, serves only to obscure the horribly damaging nature of flat tax schemes—or, indeed, even schemes that are only as progressive as the one we have now, which has allowed the very wealthy to accumulate the vast majority of all gains in the economy for decades.
That's...not a good thing. It's something we need to be working against, and increasing the progressiveness of our tax scheme (however "aggressive" some may feel that makes it) is one good way of doing so.
For instance, you could look at contribution as a percentage of discretionary income. In those terms, you might find that the middle class contributes the "most".
The Republicans now have to officially go on record opposing it which means you can use it as a campaign issue when running against them. If you then win a majority while having raised the issue during the campaign you can claim a "mandate" for passing it.