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Most people don't have super complex taxes, there's no reason the IRS can't just send them an itemized bill every April, that you can either attest to the correctness of, and pay, or contest by doing a full filing.

Progressive income taxes aren't what make tax filing a pain.

It should be quarterly and a bill, not a refund.

I think some countries use a different tradeoff than the US for their income tax. Instead of spending a ton of government and taxpayer time and effort to accurately assess what each taxpayer owes, the government simply generates an estimate based on what it knows about each taxpayer and uses that. They accept the reduced accuracy but it is offset by the reduced effort in determining everyone's bills. That is to say, you don't need to move away from an income tax to address the problem.

On the contrary, regulatory capture and similar issues are a necessary consequence of capitalist accumulation.

The opposite of a free market is having a government decide winners and losers. A reason why many like low regulations. Reduces governments ability to screw things up.