I don't really love property taxes, per se, but the alternatives are problematic for different reasons. All taxes carry some type of presumption of government ownership/entitlement. Taxing income discourages people from working. Taxing sales discourages people from buying things. Taxing production (i.e. value added tax/VAT) discourages production. Taxing oil and gas depletion discourages harvesting oil and gas, which sounds nice until you realize it also increases energy costs and contributes to inflation. Taxing tobacco use discourages tobacco use, which I see no negatives to, except that you can't really rely 100% on sin taxes.

Also, it's worth noting that the Feds are already taxing income so high that they've basically crowded out states from meaningful revenues through income taxation. Property taxation is generally proportional to property ownership and it's controlled at the state or local level so voters have more of a say in it. It's not perfect, but in a state like Texas with no personal income tax, the question becomes how are they going to fund their roads and school systems without any property taxes being collected. If their answer is to cut schools and stop maintaining roads, I don't think that will work out well for Texas. Otherwise they're just taxing something else.