Vacancy rates in San Francisco are very low compared to the rest of the state and the country. Rent control in SF is problematic not because it leads to vacancies but because the allowable increase is far too low, way below inflation.
The estimate is there are 100,000 empty homes in the SF area.[1]
I’ve seen an estimate of 20,000 for SF proper.
This [2] report to SF Planning states the number of empty units has doubled over time.
[1]https://www.sfgate.com/realestate/article/An-estimated-100-0... [2]http://ternercenter.berkeley.edu/uploads/CR_Final_2.3.19.pdf
Even if that was added to the vacancy rate, that would still leave SF with around the national average (~7%) vacancy rate, and that's without counting the off-the-market housing anywhere else in the average (and not double counting actual on-the-market vacancies everywhere else, either.) Anyway you cut it, SF has a low vacancy rate/rate of empty homes.
Not saying it would solve the housing crisis, but adding another 20,000+ units onto the market would certainly help.