You can't really compare a single municipality to several that collectively equal it's size. The latter case has a whole lot of more localized and conflicting political interests that serve to hold back the area as a whole.

Note New York City has less of these issues because over the centuries it gained control of its neighboring areas from other counties, something San Francisco never did.

But given how fervently anti-development San Francisco itself also is, would it even have helped?

San Francisco looks positively pro-development compared to places like Palo Alto. At least they allow townhomes, not requiring detached houses with large lots. If more of the Peninsula were even near SF levels of density, the housing issues would be a lot less severe.

I know they're different politically - I'm comparing the results, which are terrible.