I think you are wrong about what adding 200k housing units would do to SF.
The 2015 building permits survey. Basically, each permit is a unit, be it a single family, or a unit in an apartment.
3 columns are total units, single family homes, multi-family apartment units
New York-Newark-Jersey City: 86424 11167 72887
Dallas-Fort Worth-Arlington, TX: 57146 29038 27606
Los Angeles-Long Beach-Anaheim: 34034 8447 24271
Houston-The Woodlands-Sugar Land: 56901 36786 19798
So, to summarize, they are building 72887 units in NYC metro, 27000 in Dallas, 24000 in LA, and 20000 in Houston this year. SF is way down the list at 8,000 units. So these are all large metro areas, but builders really don’t build huge numbers of apartment units in sprawl locations on the edges of suburbs, so most of these are infill units comparable to SF.
So maybe you couldn’t build 200k units in one year in SF, but you could easily pull it off in a decade. And all the apartment units being built in Dallas, Houston, Austin, Atlanta, and Denver are really people who should be living in SF or NYC but don’t have a choice.