Property tax is regressive and nobody should be forced out of their own home because of rising property taxes that might only be due to a housing bubble. I don't see the problem.
Capping property tax increases is similar in effect to rent control; it benefits people that were already there at a given point in time and hurts everyone who moves in afterward (proportionally).
Freezing property tax ends up being wealth redistribution from the entire rest of society to landlords as the article walks through. Second order effects also end up locking up the housing market as a whole and pushing prices ever higher making everyone worse off in the long run.
Then read the article. The problem is that in reality the money flows from low income to high income households. So it works the opposite of how you think it does.
It's a move where the end-game is feudalism.