You're right that the same arguments apply throughout the Bay Area. That fact that SF needs to build more and denser housing doesn't excuse Palo Alto, Mountain View, Berkeley, Oakland, etc. from doing the same.
But even the housing policy you describe, in which SF acts unilaterally, would still be a great good. Tens of thousands of people previously priced out of SF would now be able to live in the city. And those who still couldn't afford the city would find it much easier to live within a reasonable commute.