Or unoccupancy tax. Forcing landlords to let at the price renters are willing to give will probably do some to reduce rent levels.

Same goes for commercial, but in that case, I'd even suggest forefeiture if you are not reducing requested rent within a year of vacancy. Let someone else take over if you overspent.

Where does this misguided theory that there are vacant homes in desirable areas come from?

All data indicates it's not the case, as well as common sense.