Multiple good things would happen without prop 13:

People would move more instead of being locked in to a low effective property tax.

The tax burden would be much fairer: instead of the police and schools being funded by newcomers, everyone would be contributing their fair share to fund the city, instead of the longest tenure residents mooching off the rest of us.

Unproductive use of land would be discouraged. If a tract became highly desirable, it would be expensive to let it sit in an unproductive form

Cities could raise taxes as high as their residents wanted them to be, instead of being limited by the opinions of non-residents. Some people want to have better funded police and schools, and local government would actually be allowed to deliver that. Citizens who didnt want to live in expensive cities could vote with their feet to cheaper towns.

I've never heard anybody say anything like that when criticizing prop 13. It usually has more to do with housing prices and the fact that 2 people with the same home value should pay the same in property taxes. If you wanted to create a hereditary landed gentry, it would be hard to come up with a better policy to achieve that than prop 13.

To keep tax revenue equal, property taxes for those who purchased recently would go down, and property taxes for those who’d purchased in the past would go up.

The housing market would become more liquid because people would move out of homes if their values rose too much and they could no longer afford the taxes. This would be a shock initially, but over time it would just be seen as part of life like it is in other areas: mostly, empty nesters would downsize to a cheaper, smaller house with lower taxes. Gentrification might be more problematic though.

In practice, probably some phased rebalancing would have to happen to avoid the sudden economic shock, but, politics notwithstanding, it’s not crazy to suggest it could be done and that the end state might be overall ‘better’ for most people. The end state would be how property taxes work almost everywhere else.

Prop 13 massively distorts the real estate market and creates some strong incentives for home owners. Those distortions and incentives would go away regardless of whether abolishing Prop 13 led to a net increase or decrease in total taxes.

It would increase liquidity in the housing market.