It would be interesting to apply the existing anti-monopoly rules designed to prevent Nestlé from buying all the water to the companies who are buying all the houses.

Knowing the deep aversion to risk the owners of these companies have I guess it would only take one successful ruling to discourage pretty much the whole market and significantly reset house prices.

Private landlords would take a bit more finagling given that renters also dream of one day owning multiple homes they can rent out but maybe one could sweeten the pot by finding ways to help folk retire more easily?

Implementing this may take winning a national election and a non-trivial amount of social engineering but it's not like it hasn't been done before in other places at other times.

I do like your ideas.