I'm no expert on the Bay Area, but there's this thing called San Francisco (pretty urban mostly), this thing called Oakland (pretty urban mostly), and then some stuff to the south of SF (not so urban), some stuff north of Oakland (pretends to be urban, but isn't so much), and then some stuff west of SF which I don't know at all but think isn't very urban.
Anyway, forgive me if I'm getting my geography wrong. It isn't especially important for my point. The point is that "allow more housing in the Bay Area" is less about "why can't we build more skyscrapers in SF," and more about "why is there all that really low density stuff just south (and elsewhere) of SF." You can get a lot of density without skyscrapers. Less required parking, smaller required setbacks, smaller mandatory lot sizes...