I don't see how the fact that someone might be on a fixed income makes it fair for their children to inherit the house and tax-basis from 50 years ago.

Also, I don't see why property tax increases for existing homes couldn't be capped in some way (say no more than inflation) to make this situation reasonable for people in the scenario you've laid out. But just saying, "Your taxes will never increase again as long as you stay in your home," hardly seems reasonable.