Including prop 13 as a tax is extra, like including private school as a tax in places where the schools are bad. Possibly relevant to cost of living, but not a measurable tax.

The killer with high property taxes is that you have to keep earning more as your property increases in value, or there is a real risk of you falling behind. Similarly if you are ever unemployed you might prefer a tax proportional to your income. Obviously this also makes retiring early even more difficult. But there’s a system to suit every need, I guess.