Imagine two hypothetical cites, each with one million residents. The first one has half a million apartments, while the second one has ten million apartments.
Which city would have cheaper apartments?
Here's a better question: under a realistic model of building, where building slows down when landlords and property owners feel they have maximized the profit they will get out of it, by what date do you think housing prices will be low enough that current residents who rely on rent control to stay in SF will be able to live there again? 2025? 2035? 2050? What is your recommendation for those people in the meantime?
Nobody is "kicked" out because nobody has an intrinsic right to live in a particular neighborhood. Arguing such a thing is in complete opposition to a free market.