> This is a great time to call out California and its Prop 13 (1978) where property taxes are capped at 1%ish and can grow no more than 2% from time of purchase.

This is incorrect.

It's limited to an annual increase of 2%. That's still limited, but far different from 2% of the original purchase price.

https://www.californiataxdata.com/pdf/Prop13.pdf