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So you still have renters paying property taxes.

Renters are the controlling party. Landlords are the restricted party- they can not rent to other people or use the house themselves.

In a supply-restricted markets taxes and subsidies are ultimately paid by a supplier independent on who actually transfers the money to government.

Sure, but that doesn't preclude crappy government tax policy having an impact on markets.

Consumption and supply is not fixed and taxes aren't a free lunch.