First - there is no such thing as 'under built'.
A community can house as many people as it houses - and that's that.
There can be an 'amount of new development relative to other places' - but not without a massive dose of 'housing ideology' can you say how much is over or under.
Second, the notion that 'there was less building for decades and then a lot of building, but not enough to catch up' doesn't really make sense, because even with an ideological view of 'how much is correct' there can be no such thing as 'pent up unfulfilled demand from previous building'. There are not a bunch of people living in Calgary or Seattle 'waiting' for the opportunity if only affordability was there.
Plenty of places in the world are 'more expensive' than neighbouring regions and yet don't 'build out quickly'.
Lastly, and most importantly, Vancouver has built up quite dramatically over the last two decades, and even as it has done this, affordability has plummeted.
The problem with 'NIMBYism and Housing' is the degree to which that position is ideological and that people don't recognize it as such.
There is no such thing as 'over/under' building for any specific community, there is only such a thing relative to net demand in nation for example that is either growing or shrinking for natural reasons or migration.
Yes, there is. In a regime of rapidly increasing life expectancy, there is a demographic certainty of future housing needs.
Nobody has been able to put forth a single reasonable argument for why SF must tear down their homes and put up apartment buildings other that 'because it should'.
And FYI there is no housing shortage in the US overall, there never has been, housing has expanded commensurate with population.
Not only that - housing is relatively cheap in the US.
Of course there is a lot of demand to live in SF vis-a-vis Sacramento, there always will be, but otherwise, there isn't any reason to build a single home unless the residents want that.
If you mean to say 'people have a moral right to live in the city they were born in' - fair enough - but this notion falls apart instantly unless you want to somehow give 'born and raised SF' kids some kind of literal non-market advantage.
If you live in an 'expensive place' then your kids can live there, as long as they are wealthy enough, that's the cost of living in a wealthy place and there's no way around it.
By 'building more to facilitate affordability' - well that certainly would enable more people to live there, but the demand will come from all over not just 'the kids of'.
SF is a small city and it's expensive, if parents want their kids to live there they can literally give them their homes. Otherwise, their kids can get good jobs or live in Santa Rosa.
There is plenty of space in North Cal.
Finally, SF residents can make up their own minds about how they want to do it. More building, less building, it's entirely up to them and nobody else's business.
Because building houses generally does nothing for prices. Zoning for managed apartments is the best way to increase the housing supply.