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.
SF is already one of the most dense cities in the USA. If the government forbids people from building housing, they've historically done a poor job at it. They are the second most dense city in the USA after NYC, and no would accuse NYC of not being unaffordable either.
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?