OTOH, many politicians do want to see the tax code vastly simplified- they want the sort of system where you could fill out your taxes on a form small enough to fit on the back of a post card.
Everyone has their favorite thing that they want exempted (farms, capital investments, social security / welfare disbursements, medical expenses, school expenses, mortgage interest, rent, etc), and there are millions who would be put out of work by it- accountants, tax preparers, much of the IRS would be redundant, etc.
All of these competing interests keep us where we are. Blaming it on the "rich people" is lacking in any sort of honest intellectual rigor.
ProPublica had to commit intense intellectual fraud recently - in their recent tax propaganda rush which is being directed by the Biden White House as part of its hike taxes program - to try to pretend the rich weren't paying their fair share. The rich and upper class are the only ones paying their fair share in fact. Everyone else in the US pays extraordinarily low tax rates by and large. ProPublica had to pretend that unsold stock assets should be called income, that we should calculate rich persons income tax rates based on unsold stock holdings (and the con-artists at ProPublica of course invented new terminology to shoehorn the fraud in), and then that we should lambast those rich people for not paying enough income taxes for said unsold stock. What a joke.
All that's going on right now is the culmination of decades of wildly irresponsible fiscal behavior in Washington DC, and the bill is finally coming due, so they have to drastically increase taxes just to keep the government solvent and to keep the entitlement programs from collapsing. To assist with that agenda, outlets like ProPublica are willing to lie as much as necessary to spin whatever message is required to get the job done.
I don't think the fact that Peter Theil has a billion dollars hurts me in any way, and no I'm not some unrealistic person who thinks that I, too, can be a billionaire! Only a petty person would be disturbed that someone else has more money than him. It's not a zero-sum game. The fact that there are some outlier billionaires doesn't hurt the ordinary Joe.