Prop 13 was voted in by people who did not understand the long term ramifications of what they were doing. All they heard was "lower taxes!". The partial repeal of Prop 13 on the ballot failed (and the expansion of it passed!) just this November, again by people who don't understand the ramifications of what they are doing and just hear "lower taxes!".
Prop 13 is single handedly destroying this state. 49 other states manage to get by without an equivalent and don't have old people getting priced out of their homes from tax increases. Yet somehow that is the red herring people use to keep Prop 13 around.
Because of Prop 13, people won't sell their house, middle class people are subsidizing rich people, and in some cases, the profit being made on rentals is purely because of the low tax. If not for Prop 13, the rental would be breakeven and it would make more sense to sell.
Prop 13 also encourages people to vote against expansion in housing supply, because they want their home price to go up, up, up! Especially since their property tax will be nearly flat.
Local areas are starved for money because of long term owners. Here in the Silicon Valley I have found homes valued at over $4M that pay less than $1000 a year in property tax (whereas someone just buying that home would pay about $30,000).
Pretty much every problem in this state can be traced to Prop 13. Everything else is just a poor workaround.