San Francisco + older bay area cities are a prime example of being a bastion of free market capitalism in the guise of progressivism.
The main reason SF is unaffordable is that the city government forbids people from building housing, which is the exact opposite of a free market.
The real problem is that more people want to live in SF than they have allowed housing to be built for. But it isn't clear that if they went with Houston-style "anything goes", would they still be that desirable? Or only as desirable as less popular Houston?
1. 2,251.1/sq mi Los Angeles-Long Beach-Santa Ana, CA / 12,828,837 2. 2,156.5/sq mi New York-Northern New Jersey-Long Island, NY-NJ-PA / 19,865,045 3. 1,614.4/sq mi Trenton-Ewing, NJ / 369,526 4. 1,303.6/sq mi San Francisco-Oakland-Fremont, CA / 4,466,251
Bay Area density fairly well correlates to SF's density, actually (yes, not as dense, but neither are the metros around the other dense cities).
More housing is always great, but I think it is really idealistic to think that building more housing in a hot area is going to bring prices down much, if at all. Literally, anywhere in the world, that simply doesn't happen. At best, we get a place like Berlin that has a nice economic bust that brings housing prices down for awhile (and then they start ticking up again as the economy improves), or Tokyo, where a country-wide baby bust coupled with anemic local wages and a huge 1980s housing boom hang over, keeps things reasonably priced.
Nope. Tokyo's population is still growing, and 1980s housing in Tokyo is deeply undesirable. The reason Tokyo has sane housing prices is that it continuously builds large amounts of housing, because they haven't made it de facto illegal the way too many places have. Sometimes that's all it takes.