You can also do this with combinations of renter protections + owner-occupier protections.
Currently the latter (whether the recent trend of red states lower property taxes, or Prop 13 in CA) is much more broadly-popular in the US than the former.
Property owners generally show pretty little empathy for anyone else wanting that security.
I go the other way: nobody should be forced out of their home because other people who have more money than them decide to increase the paper-value of their home. Something has to give between "I have a lot of money, I want this place" and "I was already here, I want to stay" and I think incumbency and stability is a better tiebreaker than "money wins."