I guess you have never read anything about the various flat-tax proposals. There have been several, and they have all accounted for those with lower income levels.
One of the fundamental tenets of the flat tax is 14th Amendment "equal protection." Is it constitutionally acceptable to treat a rich person differently from a poor person? The flat-tax people say no. Progressives say yes. I do agree that a progressive tax system has merits with which I agree, but I also think it's perfectly reasonable to assert that falls afoul of equal protection, and therefore should either be rejected or an Amendment should be presented and passed to account for it.
Progressives tend to turn this distinction into a moral argument about fairness, which is not how a government that is bound by law is supposed to work. If you want the government to work on a moral basis, don't be too surprised if a later government with different moral frameworks do things you don't care for.
>Look up Grover Nordquist
Somebody else brought him up in a comment. Taking your assertion at face value, you have one data point suggesting the right doesn't want to simplify the tax code. Good job, but I've got a competing data point of Paul Ryan, who was an actual Congressional leader in the Ways and Means Committee talking about the flat tax, and not an activist gadfly. I think my singular data point carries more weight than your data point.
As for Paul Ryan, he proves my point. His proposal included a huge break in corporate rates in exchange for a modest break in middle income taxes.
And the proponents of a flat tax would say "so?"
There's a fundamental ideological incompatibility here and unless one side stops caring or puts the other in the ground the bickering will continue.
You know, the one where a single mom with children to feed pays the same percentage of her income as the single billionaire that wants to buy a 3rd yacht.
Look up Grover Nordquist. He has devoted his life to making sure paying taxes doesn't become too easy. And he ain't no lefty.