Fixing a housing crisis is easy. You just need to specify the constraints and solve for them.
First, pick a set of laws on land use that would actually work, more or less forever, to let your city grow organically and attractively, without needless sprawl and giving people the chance to walk if they want to. @ProfSchleich at Yale and Prof. Lee Anne Fennell at Chicago have given some ideas. Remember to fix the collective action problems that Mancur Olson described.
Second, look for a reform that gets nearer to that and will win votes (net) at every relevant election for the politicians in power who enact the reform.
This part is crucial but amazingly often forgotten. Politicians like ideas that win votes. They do not like to lose votes.
Remember that homeowners are probably a voting majority in your city and that even some non-homeowners may not want to see market rents go down. Even market-rate renters sometimes vote against housing near them, especially if moving is inconvenient or if gentrification might drive up rents locally.
Clue: reforms that benefit existing individual homeowners in some way, such as giving them rights to add more built square footage on their land, are often an effective way to create a majority coalition in support. If, like San Francisco or London, you have huge latent demand for housing, there are reforms that can make nearly everyone better off, including current homeowners.
If you can't find that reform, go back to step one and find another option.
Third, spread the word about your vote-winning reform until a smart politician hears it and steals it.
Repeat from step two until you have permanently fixed your housing crisis.