Here's an idea on how to simplify.
The IRS sends you a summary from all your various W-2s and 1099s for the year. It has two numbers: what you earned as income, and how much you already paid for income tax this year.
And it sends you your tax form. If you earned less than the median annual income for this year, you owe zero. If you paid anything already, you get all of it back with the enclosed check.
If you earned more, you see the result of the automatic calculation, such as tax( income ) = max( income - median_income, 0 ) x tax_rate . That's an easily-calculated, slightly-progressive income tax, with only three computation steps. If you paid more than what you owe, you get a refund. Otherwise, you could, at that point, file the forms for additional politically-motivated deductions or credits, or just pay the difference and be done.
This has the notable advantage, thanks to using the single, easily-determined statistic of median income, of cutting the number of tax filers in half--specifically the half that would otherwise pay the least amount in tax. And that half can gleefully vote for the reform! Them along with the median-plus-one person constitute a simple majority in favor.
Anyone can sit down and come up with a better way to collect income tax from the perspective of the tax-payers. Anyone. Yes, even that guy. The problem is that the tax-payer perspective is not a factor when it comes to implementation. At that point, it is the perspective of the tax-collectors that matters. And from the perspective of the collectors, a system that offloads all the work onto the payers, and where any mistake at all could generate more tax revenue, is simply perfect. And the more confusing, the better, because unclaimed deductions increase revenue, and honest mistakes generate penalties.