Yes there is. You own a more valuable asset, so now even if you want to keep it you could take out a loan against it for a greater amount than if it hadn't appreciated.
You mean take out a loan to pay for the increased taxes? The banks win with that one. Some people, especially as they age, are seeking out simplicity with their finances amongst everything else.
Your statement is based on assumptions that just don't hold for many people. First and foremost, you imply a subjective utility of receiving a loan. For many people, having loans - especially collateralized against your home - has negative utility, not positive. Case in point: someone who'd need to take our a loan to pay the property tax.
But even if you were right for the majority of home owners: feel free to tax collateralized homes as commercial property based on the volume of the mortgage. Case solved.