1) raising rates and otherwise making money more expensive encourages capital to do something else with their money than speculate on real estate cheaply, which was a pretty appealing option over the last 5-6 years (let alone the last 2).

2) it's a mistake to rely on interest rates alone to address issues here. There's a whole raft of policy issues that should be brought into play here: progressive taxation by ownership volume and vacation-rental usage, better interest breaks for first-time homebuyers, encourage owner restoration and discourage investor-flippers. BUT every other way of addressing the policy is actually harder politically, since one party sees inequality as feature-not-bug and will actively fight attempts to address it (especially if it represents a win for their opposition), and the other has both a tenuous hold on power and a coalition that may not be all on board.