The problem in SF isn't that we couldn't build up more - we certainly could. It's that you generally have to tear something down to build something up,. I live in one of the less fashionable parts of SF that is zoned single family, though it is somewhat dense by American standards (small lots, no space between houses, though each house does have a small backyard). Most of the houses were built in the 1920s and are in my opinion architecturally interesting, though of course opinions will vary. I suppose we could allow people to buy up a block or a bunch of houses, tear them down, and replace them with 6 story (or higher) apartment buildings.
While there is a case to be made for allowing this, I think it's probably the weakest place to make your stand against the lack of new housing construction in the bay area. We have options other than tearing down some of the oldest neighborhoods west of the mississippi.
While everyone may be saying Not In My Backyard, there are degrees of NIMBYism. Personally, I think that it's far more egregious for very low density areas like Mountain View or Menlo Park to ban new housing development, especially when these are the same cities that have green lighted office construction that will bring hundreds of thousands of new workers to the region.