Prop 13 is a nothingburger. Median homeownership period in california vs nationally is only like 2 years longer. It shouldn't be affecting costs that much in other words since median property is back to market rate every 15 years or so.
And what costs are we talking about anyhow? Tax shortfalls for local government? Decades later that has been rectified through other taxes and funding mechanisms and we still get new roads and schools in california. Housing costs increasing? I would say the fact that cities today are zoned within a few percentage points of present population levels (vs zoned for 10x present population levels pre 1970) is the actual source of that sucking sound from the chest.
That's not really the point. Prop 13 is known to be a huge disincentive to efficient transfers in home ownership - people will strenuously avoid selling their homes and buying something that's closer to the kind of shelter they actually prefer, because they might have to pay a higher assessed property tax if they did that. These effects are very real and well documented.
Prop 13 wouldn't lead to those incentives if property prices didn't increase so aggressively. Once again comes back to zoning as the root cause. Is prop 13 bad? Only in the face of inappropriate zoned capacity, it seems. Which begs the question of what prop 13 removal would even do in such a situation? Zoning capacity isn't changing so prices will still go up beyond what is affordable for the median worker. The only thing changing is people won't be insulated from that rise at the end of their life when they are on a fixed income is all. Does that solve the housing crisis? No, but it does ensure more people are regularly displaced from their homes.
Property prices are increasing so aggressively because assessed property taxes are low and people are significantly deterred from selling.