SF is one of the most dense cities in the US. It’s pretty dense... If you’re expecting manhattan then that’s never going to happen and you should let people know Manhattan is the only place you consider a dense city.
There is a lot between SF and Manhattan in terms of of floor area / land area. The difference doesn't show up as obviously in the residential numbers because Manhattan has so much commercial relative to residential usage.
Paris or Seoul might be good goal posts for SF and the Bay Area; even outer-borough NYC is still more dense. Without arguing the merits of preservationism one way or another, SF could "look" the same and be a lot more dense if:
1) Garages are converted to apartments. Easiest and cheapest for the housing itself, but requires much better transit
2) The Sunset is raised up to not be shorter than the older parts of the city. Yes, that's a big change, but I think people are less sentimental about the little ticky tacky boxes than Victorians.
I find it vary interesting how old apartments like https://en.wikipedia.org/wiki/Consulate-General_of_Russia_in... amid a see of single family homes point to how before post-war suburbanization everything was set to densify with a look and feel like the tenderloin (the buildings themselves, when they were new, don't hate). Even the 60s modernist towers on e.g. Russian hill, for all their excessive parking and other issues, are bigger.
The thing to remember is NYC wasn't so different than the rest of the country pre-war. Rather it was farther ahead on the same trends, and when the trends abruptly reversed it was left was a critical mass of good transit to sustain "real urbanism" through stagnation and bad policy, while other cities weren't. Only after all that did such a stark dichotomy emerge.