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.