A major problem with decoupling property taxes on owner-occupied housing from market prices is that it removes the biggest incentive for a homeowner to vote for policies that keep the local real estate market in check. An owner occupied house in a desirable area where there is no disincentive to politically engineering a supply shortage becomes a financial investment. Any increase in housing value becomes profit for the owner (or their descendants). This leads to supply restrictions and escalating prices and an increasingly unhealthy society as the young and the poorer are pushed out of the city, county, or even state.
This is essentially what has happened in coastal California over the last 60 years.