The funny thing is: you just explained why property taxes are basically 'free'. (They are basically the best tax. Tweaking them to include only the value of the land, and not the house makes them even better.)
Basically, supply and demand in the housing market determine the sum of property taxes plus mortgage payments. If property taxes fall, real estate prices increase until the sum is the same as before.
If property taxes increase, real estate prices decrease accordingly.
Of course, existing property owners will feel the changes in price. But for someone young or from outside the area, who doesn't already own property, areas with high and low property taxes cost the same amount to live in.
The area with high property taxes can either spend more on public infrastructure or lower other taxes.
In the long run, all of society is made up of people who don't live yet today.
In the short run, votes are mostly cast by people alive now, many of them owning property.