I've heard SF's laws against denser housing are a major factor in the housing "shortage" there. [1]

In NYC, rent control laws are a major factor in the artificial housing shortage. There's a consensus across economists of all stripes that rent control is a bad thing ("the most efficient technique presently known to destroy a city -- except for bombing"). See the studies cited here. [2]

[1] http://pandodaily.com/2012/12/01/san-francisco-can-become-a-...

[2] http://www.econlib.org/library/Enc/RentControl.html

What you say about rent control is true - if there are not restrictions on building new housing. This is almost never true.

The question is: Would SF be as popular without zoning laws? If there were 50 story towers in the middle of the painted ladies, would it still be SF?

Or maybe I'm confusing zoning regulations with other codes.