I'd argue you're mostly getting cause and effect backwards: places end up with lots of high rises because they're the most economically productive localities. Obviously at the margin another high rise will lower prices a bit, but the rate at which we'd be able to build them in SF sans restrictions would at most keep prices stable year-on-year. Which isn't nothing, but it's important to be clear that no one making, say, $80k a year will ever be able to purchase a house or condo in San Francisco, regardless of our policy choices.
There are lots of places either similarly, or more dense than San Francisco with housing people can buy on an $80k salary. All of these places allow for higher density housing. Sure SF is way behind the curve at this point, but it's a bit silly to argue that "policy debt" is a reason policy changes wouldn't do much.
I'd argue you're mostly getting cause and effect backwards: places end up with lots of high rises because they're the most economically productive localities. Obviously at the margin another high rise will lower prices a bit, but the rate at which we'd be able to build them in SF sans restrictions would at most keep prices stable year-on-year. Which isn't nothing, but it's important to be clear that no one making, say, $80k a year will ever be able to purchase a house or condo in San Francisco, regardless of our policy choices.