“ the price increase on paper means is that I pay more property tax”

In almost all jurisdictions that’s not how property tax works. You’d only pay proportionally more if your home went up more in value than your neighbors. Also, property tax goes up on rentals too, it’s just baked into the rent vs something a separate charge. In the US the homeowner gets to deduct all or part of that tax from their income taxes while the renter must pay that with after tax dollars.