1939 said:
California's property tax system is not the reason why housing is so expensive.
It isn't the sole reason, but it's a very big part of the problem. Prop 13 heavily distorts the housing market by disincentivizing buying and selling as values rise, but also heavily incentivizing restrictions on residential zoning encouraging commercial development to drive sales tax.
The longer you stay in house in Cali, the more expensive it is to move anywhere in the state. If you bought 15 years ago, the median home price in California was $253k. Now it's $880k. If you move now, your property tax triples overnight. It makes sense for people to hold on to property and land, which means an already finite and in demand resource gets more expensive.
But what's worse is that a freeze on valuations means taxes supporting police, fire, EMS, utilities, and basic city services don't increase with inflation or the costs of providing those services. Commercial property, on the other hand, has a higher tax rate and generates business and sales tax. That means commercial zoning generates more income to support city services and becomes preferable to residential, artificially constricting the available housing market.
It also means there's a disincentive for more dense residential usage. More dense usage means infrastructure and services upgrades to handle the increased usage and density, but you run into the same taxable value problem. If anything, it's potentially worse because a shell company could own the property and itself be sold in lieu of the property, locking in the property tax revenue indefinitely. A lot of developers create holding companies to fund construction and isolate any potential failures or losses, and the property can simply be left in the holding company's possession and sold with it.