The problem comes when you realize what you have to do to get a vote, which is to buy a house. If you can't afford to live there then you can't vote for policies that will reduce housing costs there because you aren't a resident. And once you have a vote because you own a house, now you want housing prices to go up rather than down.
There is no way for the people who need less expensive housing to vote for it, and the opposite incentive for the people who could vote for it to actually do that.