Population growth is reduced by a housing shortage because people who otherwise want to move in can't if there aren't units available for them to move in to.

Moreover, who is supposed to have a monopoly on housing in San Francisco? Is there any single entity that owns even as much as 1% of all the housing in the city? And even if there was, wouldn't building more housing still fix it, because the more you build the more you dilute their monopoly?