> You don't give a source, so it's unclear whether that figure accounts for Prop 13 effects
Since Prop 13 both sets the maximum rate of property tax and sets the procedural requirements for increasing any tax in California, everything about property tax in California is “Prop 13 effects.”
I suspect what you mean is “effects of the Prop 13 limits on annual assessment increases”.
> The average of existing tax bills (with embedded Prop 13 reductions) is meaningless for comparing to new-property taxes in another state.
The point wasn't comparing new-property taxes, it was addressing “how other states manage to do the same work the California Government does (having schools, roads and police) with much lower rates of income and sales tax and a much less smaller [sic] tax base.”
One of the ways they do it is by having higher property taxes. Often at effective tax rates higher than the prop 13 limit on nominal rates, even before the effect of assessment limits. (And, in the broader context of the thread, consideration of moving out of California, if the alternative is staying in place in California, property taxes with the Prop 13 assessment limit are absolutely the right comparison with new-home taxes in other states.)