That's a rather glib leap of logic.
The 'shortage' is often simply substandard and/or dangerous dwellings due to corruption, theft, lack of code/code enforcement, etc.
If your problem is overpopulation, then creating more housing to accommodate even more overpopulation is madness. It's the fish-grow-in-proportion-to-aquarium phenomenon. Surely birth control and a cultural shift away from breeding like minks takes priority?