Comparison with Manhattan is unhelpful. I think better comparisons are Singapore and Tokyo. Bay area residents bristle st the idea of tall towers --specially given the geological faults running beneath. Given that, Tokyo's approach of midrises interspersed with highrises would probably be the best hope. We could at least double or triple the population in SF proper. It would help tremendously if surrounding cities also went on a construction binge to relieve pent up demand.
It helps Manhattan a lot that it has one of the world's best-engineered public transportation systems to connect it to the other boroughs and to Jersey.
The problem with construction booms in East and South Bay is that the transportation infrastructure in SFBA is barely keeping up with the population as-is, and however asymptotically it approaches "adequate" today, it is also one of the country's most poorly managed systems: it's underinvested, hemmed in by a dysfunctional political system, freighted with union, tenure, and retirement problems, and poorly maintained.