If you can only build 10 houses, and make 10% commission... are you going to build a shack? or are you going to build mansion?
The houses that get built, if the gates were to open wide, would all start off on the high end... while that would start a downward pressure, it would still be a very long time before those who can afford $200k for a house see anything in their range built.
What happens is that 10 people move into those new places and 10 people move into their old one and the vacancy works it's way down the line. Eventually some guy down the bottom gets slightly cheaper rent or a better place.
Imagine that instead 100,000 high-end apartments were built in the Bay Area. None of them will have poor people move into them but instead places like (to quote elsewhere in the thread) "downtown PA (university Ave) its right around $2800-3000 for a 1 bedroom, for places with 20 year old appliances and no upgrades." might now be $1000/month cheaper and affordable by somebody on a lot lower income.
Telling people that within 10-15 years if you keep building several hundreds of thousands of houses eventually rents will be affordable is not a winning slogan :)
New housing would start off being expensive because all housing in SF is expensive. Not the other way around.
Maybe the root of this fallacy is that it assumes prices are constant. If you build something today and charge $5k/month for it, that's how it will somehow remain forever. But in reality prices are set by supply and demand, for both new and old housing.