There already is. Some cities, including the expensive cities in the U.S., make bank collecting property taxes on vacant units- units for which the city provide

There already is. Some cities, including the expensive cities in the U.S., make bank collecting property taxes on vacant units- units for which the city provides no schools, transit, trash collection, healthcare, water, or any other services because no one lives there. It's free money! The rational course of action is to not only not levy a tax on empty units, but to encourage as many empty units as possible! Collect property taxes without the overhead of futilely trying to figure out which are vacant. Then let the free market build housing to make up for it. This is what New York City is doing. Remember that the housing market is a market. If you magically appear 20K units out of nowhere, prices will go down for a while until 20K units don't get built that would otherwise get built and prices then end up right where they would have if you didn't magically appear those units.