This is a terrible idea. How about actually do something about the private interests buying up all the housing & then putting it up way over market prices, or just fabricating market prices (aka fixing prices).
Not to mention giving religious institutions a way to move people around the country in order to change the political climate around them. You local government not bending the knee to your stupid religion? Just build some housing, and move in a bunch of worthless families from some religious hellhole, and boom, you’ve got more political capital.