In a city like SF, vacancies is not a thing. Actually for that matter, in any market the market price is some equilibrium price that gives a certain vacancy rate.
"Affordable housing" is a completely separate issue.
As you mention, a significant percentage of tenants with rent control would be regarded as "high income" households.
Hell, I know a guy who has a rent control units for a couple decades. He can pay his monthly rent with one day's take-home pay.
It sounds outrageous, but I know someone like that too. Got a rent controlled box in Berkeley as a student, never left. Rent is only about $700 a month now. If you make $180,000 a year, that's a single day's pay.
Not to mention the homeless.
Don't get me started on the housing "market" and rent control impact on supply/demand. Housing is largely an adversarial game, not a win-win game.
Here is one of many papers: http://www.socsci.uci.edu/~jkbrueck/course%20readings/gyourk...