I prefer Texas's solution to that problem, which given my leftish politics, doesn't happen that often. :) In Texas, people over 65 can stop paying property taxes entirely, but the taxes are not waived, instead they're just deferred and accrue as a lien on the home. When the home is eventually sold (either by them, or their heirs), the taxes are paid out of the proceeds (the state eats the remainder if the proceeds are less than the back taxes).
This way a retired person never has to move because of an increase in the value of their property making the taxes unaffordable. But if and when it's sold, and they actually realize that gain from the property's value, at that point they do have to pay the taxes. Proposition 13 instead lets them have their cake and eat it too: they pay property taxes as if there were no value increase, but then can sell the property and get a big windfall.
This way a retired person never has to move because of an increase in the value of their property making the taxes unaffordable. But if and when it's sold, and they actually realize that gain from the property's value, at that point they do have to pay the taxes. Proposition 13 instead lets them have their cake and eat it too: they pay property taxes as if there were no value increase, but then can sell the property and get a big windfall.