(1) Skyscrapers are very expensive per livable sq. ft. and take long to build. Low-rises are comparable to single-family homes, so they're lower-risk for developers, come about faster, and have a lower minimum rent price (in the wonderful event SF builds enough housing for rents to go down).
(2) If you neglect the rest of the city and create a sharp density cliff, transit patterns will be wonky. SF is in an odd in-between stage regarding public transit, and creating a transit-oriented dense central neighborhood hurts commutes from other semi-car-based neighborhoods: they should be denser to justify an increase in buses and trains needed by the city.
(3) In a medium-density city like SF, low-rise apartments would make a huge difference in supply. Consider the fact that the NYC neighborhood East Village, comprised mostly of 3-6 story low-rises, is (IIRC) the 2nd densest residential neighborhood after a part of the Upper East Side, pushing over 100k per sq. mile. Because this avoids the problems of high-rises[1] (e.g. blocked sunlight, like Manhattan's FiDI), it's not nearly as unattractive to NIMBYs. The few I've met hate skyscrapers, not low-rises.
I think HN might have a skewed perception of what levels of density correspond to different building heights, and what those buildings cost (in time and money). You don't really see huge swaths of residential high-rises in Manhattan most anywhere. That's due to both quality of life and cost reasons[2]. SF doesn't need to become Hong Kong anytime soon--there's not that much demand--so it's worth considering other options for the sake of political tractability.
[1] http://images25.blocksy.com/L_2027825/122330054/original.jpe...
[2] You could argue that in the past 10 years, Manhattan has had an increased need for more high-rises. But because of cost and the cliff reason mentioned above, it turns out a big part of the cost pressure in NYC has come from an inability to build low- and mid-rise buildings in Queens (which has comparable density to SF).