I don’t think there’s any evidence at all that more housing increases birth rates. Japan has remarkably affordable housing, even in Tokyo, because of very good zoning codes, but they have a plummeting population. And sure, more housing in a given area means more people in that area, but if you force them out of that area, they’re still going to have to live somewhere. If you force them farther away, they’re more like to drive and they’ll probably pollute more as they have to travel farther to access jobs and amenities.