The only force working in opposite direction would be that some people will be able not to flock to attractive locations but I don't think it'll be enough to counter the obvious raise.
You'd have to tax property progressively and accept the drop in property price associated with it being less attractive for people who buy to rent. Apparently property prices are sort of holly cow in US so no-one in their right mind can afford doing anything that would harm that, even it it meant actually ending the poverty.