1. People are disincentivized to move - the longer you've lived in a home, the larger the effective subsidy (vs average property tax payer) becomes.
2. New homes are on the other end of that - you pay much more in taxes than the average. So the cost of new homes is higher.
3. The average home pays less than it costs the local government. This is largely true everywhere because of the cost of public schools, but Prop 13 makes it more pronounced in CA. So local governments have a huge disincentive to approve any housing, especially larger apartments or condos where school aged children could live.
4. Govs make up for the lower tax per home by charging very high development fees for new construction, which raises prices and lowers rates.
Prop 13 is no different from rent control. It distorts the market and limits supply.
If a property owner can't afford the tax on their land, it means the land is under-utilized. SFHs should be replaced by townhomes which should be replaced by multi-family buildings and so on. That doesn't happen because people who bought a house 50 years ago for a few beads and pieces of gum don't have this market signal in the form of a higher property tax bill.