One thing you left out is that people make laws to try to stop people from moving in. Those laws make it harder to build which does not stop people from moving

One thing you left out is that people make laws to try to stop people from moving in. Those laws make it harder to build which does not stop people from moving in, but makes housing more scarce which leads to higher prices. What would San Francisco look like right now if they'd allowed high rises to be built for the past 30 years?