That hasn’t really worked anywhere: popular places attract so many people that you literally can’t put supply into synch with demand. San Francisco is already a dense city, would it be as cheap as Manhattan if it had Manhattan like density? Maybe, but Manhattan isn’t cheap.
It might be better to focus more on better intercity and intracity transport like they do in Japan, or allow for smaller cheaper places to live like they do in Tokyo (incidentally, aggressively deprecating the value of structures like they do in Japan might help as well).