You're right, I thought the parent was complaining about higher property taxes, not that property taxes would increase if they were to move to a similarly value

You're right, I thought the parent was complaining about higher property taxes, not that property taxes would increase if they were to move to a similarly valued house. That does disincentivize moving into an equally valued house, but moving into that house would have the parent paying about ~2% of X each year in property taxes as opposed to ~1% of X. The appreciation of the house still covers the increase in property taxes for the next 75 years.