So you are claiming that if SF becomes as dense as Manhattan, it will be as cheap as Manhattan? Or maybe Hong Kong’s density and housing affordability is the target here?

The ideal situation is Tokyo, where a lack of culture in speculating on housing coupled with population decreases leads (going down in the metro area for the last three years) to housing affordability.

I'm claiming that the balance of supply and demand affects housing prices.

If you increase the supply by enough, that will tip the balance to where the market clearing price will go down.

The real underlying problem is that you have X million people who want to live in the quaint version of San Francisco. It's literally impossible; the quaint version dies at some point as more and more people are piled in, even if the resulting city is world-class and quite desirable.

Just like the entirety of Los Angeles couldn't move to Santa Barbara without Santa Barbara being changed forever.

The closest reasonable equivalent we can do is maintain the quaint "old town" and build a "real city" around it where people actually live and work, and the old town remains as a tourist destination, basically.

This is the case in much of Europe. The Paris you visit and the Paris people live in are often mixed, but they're noticeably different.

Rapid mass transit to city centers can hide the distinction.