There’s fairly few units that people are just letting sit unused and empty.
In 2022, 23% of vacant for-rent units were vacant for less than a month. Only 26% were vacant for more than 6 months.
There’s more vacant housing “held off market”, but keep in mind that includes housing occupied by people with usual residences elsewhere, housing that’s currently held up in legal proceedings, housing currently under construction or repair, or in need of repair. The amount that’s being held off market by Blackrock to keep prices high is tiny at best.
Vacancy taxes have been tried, and their effect is generally fairly small. That’s not to say that they’re bad, just that they’re only a small part of a larger solution.