The metro area density is mostly a measure of whether the suburbs are more or less urbanized. E.g. the LA/OC metro CSA is substantially more dense than the SF/Oakland/Fremont CSA, but nobody would say that LA is denser than SF. Rather, LA is surrounded by urban sprawl while SF is surrounded by suburbs.
What sucks more is that a lot of the new buildings are only luxury buildings going for $2000+ a month per living space per person and most have homeowner's association trying to keep the ratio of owners to renter's high, so most units don't even hit the rental market. Couple this with the fact that the only program in the city focused on making housing affordable, the BMR program, only really makes things accessible for those with a household income between 70 and 90% of the median income, leaving every else out in the cold, and you basically have horrendous conditions for most people to be able to live here.
The way I see it, San Francisco's 1% are taken care of, as are San Francisco's 60th to 65th (I don't know the exact equivalent to the 70-90% of median income here), and everyone else is left to fight over what little housing is left.
However, this problem can still be overstated. Plenty of new construction is taking place in SF.
http://www.spur.org/publications/library/article/san-francis...