> Flat tax doesn't even simplify anything.
Yes it does, depending on the implementation. There's a 2005 Economist article which does a good job of summarizing why[1].
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Fewer brackets are simpler to administer, but one bracket is simplest of all. Under a pure flat tax, the taxman takes the same cut from the last dollar you earn that he took from the first. The appeal to high earners is obvious. But the administrative elegance of such a system is not so immediately apparent. Because every dollar is taxed at the same rate, it does not matter to the tax collector how many dollars are going to whom. Thus, in principle, the taxman could simply withhold 20% of a company's payroll, without needing to know who was paid what. Add a second rate of tax, however, or a personal exemption, and the tax collector must find out how much money is going into each pay packet before he can be sure of collecting the right amount from the right person. In America, for example, the tax collector needs to tax the wage packets of 130m or more employees, rather than simply taxing the payrolls of 8m or so enterprises.
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The mistake you're making is assuming that the tax system can only be simplified on the individual level, but as the quote above demonstrates this isn't true.
Certain changes to the tax code do entirely away with the need for the government to exhaustively audit large parts of the economy.
Another quote from the article demonstrating such a case:
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In Canada, Australia and the European Union, for example, staple foods, but not restaurant meals, are exempted from value-added tax. [Therefore] hot roast chicken is taxed, but cold roast chicken is not. “Does anyone expect tax administrators and business owners to have thermometers on hand when they do their tax calculations?”
END QUOTE
In this example, by progressively taxing food you're creating the accounting problem that the government theoretically has to track economic activity down to the level of whether a chicken was warm or not when it was sold.
Simplifying the tax code does away with needing to solve that problem entirely, and eliminates some of the current incentives for tax avoidance and other fraud.
1. https://www.economist.com/special-report/2005/04/14/the-case...