There's a better way than that. The way the US tax system actually works is incredibly misleading:

1) We pretend to have an income tax but then make it work like a consumption tax in practice. Ordinary people put earnings in excess of spending in a 401k and defer the tax until they want to spend the money. Rich people defer capital gains indefinitely until they want to spend the money. It's an income tax on paper but a consumption tax in practice, and doing it that way is much more complicated than just using a consumption tax.

2) We pretend to have a progressive income tax, but then impose benefits phase outs that fully cancel out the difference in marginal rates between the poor and the rich. Convert the benefits to cash and eliminate the phase outs and you get something which is equally if not more progressive, significantly more efficient and dramatically less complicated.

So, you can throw all of that out and replace it with a flat rate consumption tax and a UBI and it would be as close to a Pareto optimal improvement as anything in politics ever is.

Which also makes a huge amount of headway against the illegal immigration problem, because another disadvantage of pretending to have an income tax is that it effectively subsidizes anyone paying people under the table since then they're not paying the tax. Whereas if people working under the table still have to pay the consumption tax on everything they buy, and they also don't receive the UBI because they're not lawful residents, they'd be at a disadvantage relative to ordinary citizens, instead of the existing system where breaking the rules makes you better off.

The tax code is inefficient on purpose. A simple uniform system is politically infeasible, due to the fact our political system relies on pretending to give special favors to every tailored interest group individually (making the tax code even bigger every time).

We arent at a loss of what to change to make it simpler/optimal. We're at a loss at how to make anyone proposing that not lose the election when everyone else is telling each group they'll lose their special carveous and how about I sweeten the deal some more.