Earlier quoted context omitted.
Prop 13 is the big elephant in the room. Repealing Prop 13 and rent control would probably align everybody's incentives to keep housing "affordable". Owners would probably welcome higher density housing to help keep property taxes down. Renters would likewise welcome more housing to increase the rental supply. However, there doesn't really seem to be a way to actually repeal any of these laws.
Problem being, a lot of people would get absolutely screwed by that, and end up losing their home. There needs to be a way to fix that, without going back to the original problem Prop 13 was intended to fix, which was people being unable to afford the property tax on homes that they had been living in forever.
Prop13 is a monster that will continue to exacerbate inequality. Families that owned homes in affluent areas pre-1970 will continue to pay artificially suppressed property tax rates in perpetuity, so long as they only transfer the house within their immediate family. In that way, Prop13 is a perverse incentive to suppress real estate transactions, which exacerbates the real estate issues we already have.