The government could just guarantee housing for a fixed price. That fixed price becomes the upper bound and all private market participants would have to bid lower than this upper bound.

This doesn't happen because those who have a political say don't actually want more housing. My proposed idea would force the government to actually solve the problem after all. If there is not enough housing the government would be forced to build it as a last resort and if the government can't do so because of the laws it has enacted then it can change those laws but that's exactly what must be avoided at all costs if you were to ask existing homeowners.

This is a lot like Singapore's HBD, which builds lots of public housing. And you're right, it's the absolute nightmare of people in SF who say they want non-market housing, precisely because it means new housing and new buildings.

However, it's a generally popular idea, that if put to a majority vote could pass. It's individual small groups that would stop it, because city politics are highly undemocratic and controlled by small factions.

However, there's hope at the state level to make this possible. I'm hopeful that in the coming legislative session there will be some serious attempts at state-level public housing to alleviate our desperate shortage.