I agree that Prop 13 is destructive and an unfair wealth transfer from the young and new residents to the house owners with seniority.
On the other hand, the only meaningful macro effect it can have is to reduce liquidity and moderately buoy prices.
A family can't upgrade to a larger house without incurring the increase, so they don't move. A family receives a better job offer... but the commute will be too far so they don't accept it. A family wants to move, but they demand a premium to sell to cover their increase of property taxes.
On the other end, a family buys a house that is far too expensive than reasonable (6x income) but does this with the expectation that their frozen property tax rate will not scale with their income and their property value. Families that aren't willing to accept this default risk miss out on being able to purchase in that area.
Both of these effects are bad but I think it only partially explains the differential between house prices and annual incomes. I assert the overarching reason is scarcity due to geographical constraints and insufficient development. If Prop 13 were a primary factor, we would see high house prices in the Central Valley and near Joshua Tree.