And voters put people in power who restrict supply and thus guarantee profits for homeowners.

With how small polities are in the Bay Area this leads this to everyone pushing the burden onto someone else. With a large enough polity responsible for zoning (e.g. New York City's five boroughs) the pressure to add housing becomes too large to completely ignore.

>Prices go up because demand is higher than supply. No other reason.

If the government mandates that the price of something is X, and X is higher than the price is now, prices go up.

Also, remember than nominal price and economic price are distinct. “Price” needs to include all tax subsidies and other incentives/ dicincentives.

No they don’t. See the USSR, real prices were completely removed from what the government set. If SF set the price of a house to 100k, people would just bribe each other the difference.