But that's also largely a factor of mostly high-income people moving in, while mostly lower-income people are moving out. Keep up the business climate that fuels the inward funnel of money, and you'll keep prices high. Even if you reduce restrictions to building supply, you'll have a game theory bit of not lowering prices in any hurry since people can so clearly afford them and are so clearly willing to pay them.
Prop 13 benefits corporations, long term property owners, and people that inherit property. At the expense of renters, new home buyers, and beneficiaries of public goods and services.
They have to live in their fabulously high priced and undertaxed home to enjoy the benefits. They can't move to another town or maybe not even take a job in the other side of town.
https://en.wikipedia.org/wiki/1978_California_Proposition_13...
To an outsider like me, this seems like one of the worst features of Prop 13. Over time it separates people into two classes: those whose family has owned property for a long time, and everyone else who can't afford to buy a house because the taxes are prohibitive. (Even if you're very rich, it will make more sense to rent than to trigger tax reevaluation.) Call it neo-feudalism.