Prop 13 also induces people to not sell their property, or convert properties into more units like you, so there are less available units on the market, which increases prices even further.
For example go look at SF or LA vs Miami on Redfin and see the stark difference in how many units are for sale at one time.
Higher property taxes encourages people to sell their properties if it's not economically worth it anymore to hold the property and give it to people who would actually use it. And it also encourages them politically to build more housing so their property tax bill does not go up too much.
If the city doesn't make enough money, then it become bankrupt. Roads, schools, sewers and police can't function properly anymore. The money has to come from somewhere!
It only matters if I decide to sell it AND move somewhere else. Which probably isn't going to happen.
You (quite literally) have a million-dollar offer on the table to move to, say, Austin, TX (or dozens of other great cities). The fact that you choose not to accept that offer does not negate the existence of the offer. The offer is always there. And this is a very real asset that you have (that, I hope it's clear, most people don't have), whether you choose to acknowledge it or not.
Value of primary residence isn't even considered part of your net worth. It exists, but it's not fungible like other assets.
Anything you own that has value, but is not your primary residence, is intrinsically different from your primary residence.
And that difference is reflected in standard financial metrics.
So now people buy in and don't move.
This is completely untrue. I have a house in 94087 where I live about 7 months/year (the other 5 months are in Tel Aviv, where it's also very expensive!) I own the house, bought in in 1989. I don't benefit at all from increased house prices. It just makes everything more expensive.
And even under Prop 13, my property tax goes up 2% a year. That's more than inflation.
I don't benefit at all from the "increased value" in my house. If I could, I'd tear down the house and build a 2-family house on the property. But even if zoning laws allowed it, the house would be reassessed at current market value, and it wouldn't be worth it to pay $32,000/year in property taxes alone. (I've looked into this to the extent of hiring a real-estate lawyer to see if it's feasible).
If there were no prop 13, people would be forced out of their homes because specu-vesters would drive the prices up making just the taxes affordable.
The solution is to BUILD MORE HOUSES. Build apartment buildings. Close by so people can walk or take existing mass transit to work. And allow people with single family homes to tear them down and build 2-family homes without being reassessed.