Prop 13 cut the tax rate below the cost of services the city provides residents. Building more housing, especially cheap housing makes the cities financial situation worse. One of the ways cities try to make up for this is by charging fees for new construction. Which also drives up the cost of housing.
Also doesn't help that prop 13 limits property tax increases for commercial property. And corporations live forever.
In the Bay Area, commercial property is often owned by shell companies. When commercial property is purchased or sold, the shell company is sold instead of the actual property so the property value is never reassessed for tax purposes.
Also doesn't help that prop 13 limits property tax increases for commercial property. And corporations live forever.