I'll answer my own question: the root problem of too high rents is that governments:
1) have outlawed the construction of enough new housing to meet demand.
2) many places (CA especially) have property taxes that are drastically too low (and in CA's case, radically unfair).
Vacancy taxes are a bad hack. As you note in your comment you have to build in all kinds of grace periods or exceptions and even these can often be easily gamed or ignored.
Cities will be much better off if they fix the real underlying problems.