I do not understand your Post. The Valuation on the House determines the Property Taxes.
If you buy in an up Market and the price of Housing falls substantially, you can get the House Reassessed to reflect the drop in Value and reduce your Property Tax Bill.
However, of the reverse is true, Prop 13 limits the amount the House Value increases to just 2% a Year.
The cheaper the House, the lower the Taxes, but the “rate” is still limited to 1% plus any Voter approved Bond Measures.
My Friends living in Texas pay 3% plus in Property Taxes but for the most part they get more House for their Money. They also get hit with yearly Assessment increased that I believe are limited to 4%. I’m sure some Texas FReepers can validate whether that is true or not.
Check the rules in Prop 13 and you will get it.