> Sf’s rent control also means tenants can’t leave
They have exactly as much freedom to leave as they would without rent control. They _choose_ to stay because rent control has made it advantageous to stay. The way you phrased it implies you're suggesting this is a bad thing for renters but that is strictly a positive. Without rent control they'd have zero affordable options, with rent control they have 1 affordable option. Woe to the inhabitants of rent controlled apartments with their golden handcuffs.
Rent control drives up rent prices for everyone.
So yes, if you have rent control in a city, it would create an environment with zero affordable options.
Obviously it does not drive up the rent price of the person who is paying less rent. That's the whole point. The residents of SF have voted to prevent you from taking their apartments, so if you don't want to bid very competitively for an already empty apartment, you'll just have to take an apartment somewhere else.