I believe that, on average, housing prices increase when housing is limited and decrease when it is not. I don't believe this relationship is nearly as linear as people imagine, especially since not all "demand" for housing comes from people wanting to live in it (thanks to rampant speculation in the market). I also don't believe that even a tremendous increase in available housing will cause the price to decrease enough that rent is actually affordable for the people who currently depend on rent control, and I am not willing to treat those people as "collateral damage" in the quest to lower housing prices in SF.
If we built lots more housing, there are two mutually exclusive possibilities (though honestly, they are on a spectrum):
A) Housing becomes affordable, or B) housing stays expensive.
The latter means we added trillions of dollars to the national wealth.
By the way, please go ahead and do tax property a lot. Ideally, you'd only tax the unterlying land with a land value tax. But even a naive property tax is OK.
That way foreigners buying up local real estate for speculation means foreigners paying for local services.