Except the supply here is necessarily constrained by the amount of land available to build on. You're treating this like microeconomics 101, which is a fundamentally flawed way to look at the problem.
Nearly 75% of land in San Francisco alone is zoned for low density single-family or duplex homes. 37% of it is just for single-family homes alone. [1]
Nearly 98%(!!) of land in San Jose is zoned for single-family homes. [2]
Replacing every ~10 single family homes with even a 6-7 story apartment building can easily increase the supply necessary to reach equilibrium, and that's ignoring the fact that you can build affordable apartments that are >20 stories (see: Long Island City, New York).
[1] https://www.latimes.com/politics/la-pol-ca-single-family-zon...
[2] https://haasinstitute.berkeley.edu/single-family-zoning-san-...
Nearly 98%(!!) of land in San Jose is zoned for single-family homes
More likely, the data says that 94% of precincts have at least one single family home.
Well over 10% of land is rights of way (e.g. streets, watersheds, etc.), easements, or is public property.
But even that could be misleading, since San Jose has massive city boundaries that includes hills and other places that really couldn't be built on regardless of what they were zoned for.
Per the parent comment, the prescribed solution is to eliminate (or heavily curtail) such zoning laws. In other words: “deregulate housing”.
For example, here in Chicago the value of land downtown is upwards of $40 million per acre. It has nothing to do with the location of the land or that we're completely maxed out for development. It has everything to do with the fact that you can build 250+ units on that plot of land.
Real estate always has to do with the location.
People will sell their homes in the market, as they do today. Today it is illegal for a buyer of such homes to build multi-story apartment buildings in their place. The argument is to simply allow such construction to happen.
You have a strange definition of "force".