Property taxes have some major fundamental problems, not least of which that using them to pay for local services tends to make such services better in more affluent areas and worse in less affluent areas. They produce potentially unbounded and unexpected expenses long after paying off the house itself (which impacts retirees and others trying to predict future expenses). And on top of that, as mentioned in the comments here, attempts to control the growth of property taxes can create major supply issues in the housing market.
So why not get rid of property taxes altogether? Most states/countries already have either income tax, sales tax, or both. Why not settle on one tax, either income or sales, and use that for all government expenses?