When I live in São Paulo, Brazil (which isn't exactly cheap and going out can be as expensive if not more expensive than San Francisco), my dad and I split the rent on a 2700 ft^2 penthouse duplex with 4 bedrooms, 3.5 baths, deck with barbecue pit, dining room, living room, family room. It was one block from Avenida Paulista on Alemeda Campinas. We each paid around $1300 to cover rent and the building fees.
San Francisco is stupidly expensive. The landlord trolls sue to block every single possible development that could alleviate the housing problems because it allows them to earn increasingly more from their real estate with little to no additional capital investment.
Buying at current levels would only make economic sense if you expected rents to keep going up. Right now, buying is a bad move unless you expect the extreme rent situation to worsen (rather than mean reverting) in the long term (20-30 years). Given that it'd take just one genuine progressive mayor to crush the NIMBYs and allow new development, I think that that's a bad bet.
Well, in an alternate reality where the City and County of San Francisco is a mayoral dictatorship (and using a suitably special definition of "progressive", though that's somewhat tangential) this might be true.
Of course, in that alternate reality, you'd still need the mayor with that preference to somehow get elected in San Francisco, which might require even a bigger divergence from the universe we live in than San Francisco having the kind of political structure which would empower a mayor alone to impose the changes you describe.