Funnily enough though, I would say that Montreal has less of a supply problem, despite being on an island with no room to expand into an infinite suburban sprawl like the bay area has. Construction still seems to happen here. People are bitching that too many condos are being built, but I think more supply is good.
Anyway, I think rent control can work pretty well, as exemplified by this Canadian city. At the very least measures to prevent surprise rent tripling while someone is renting an apartment are very much a good thing. Sidenote: I think that rent control can also help prevent property price explosions. It makes no sense to buy an apartment for over a million dollars when its rental value is only 1000/month.