Pretty sure there are plenty of houses sitting empty or as holiday rentals. Second homes, airbnbs, etc. Those could be simply banned or highly taxed and the shuffling of ownership would happen naturally.
The other problem is this, if you banned short term rentals _entirely_, which NYC basically did, you have not changed the fundamental supply vs demand structure. You still have X people who want units and Y units. Rents did not go down _at all_. House prices did not go down _at all_. The primary change was that hotel prices went up because of lack of competition.
Seems like for NYC, it worked as expected with the increasing hotel prices. And didn’t work as expected for rentals. The next step now would be to ask why it didn’t work as expected for rentals while it worked as expected for hotels, not just concluding that the ban wouldn’t work.
All data would indicate otherwise, and why shouldn't short term rental or vacation properties exist?