It depends on how supply is increased. If you allow single-unit housing stock to be converted to multi-unit, that causes existing homes to rise in price as you

It depends on how supply is increased. If you allow single-unit housing stock to be converted to multi-unit, that causes existing homes to rise in price as you say. But rezoning industrial buildings to high-density residential causes existing homes to drop in price. I believe the solution in SF will mostly be the latter, such as converting warehouses in the Mission into lofts. Also, California's weird laws mean that property taxes don't go up much even when the value of houses rise a lot. So most NIMBY homeowners are genuinely defending against property values dropping.