We absolutely have an artificial housing supply shortage, that is induced by homeowners loving 15%+ year over year housing market increases and not wanting the undesirables to move in or be able to afford housing in the first place.
It would be so much more simple to say you can just buy a lot for maybe $25000 and put one of these garden sheds in and live on it https://www.costco.com/stonecroft-12'-x-10'-wood-storage-she.... There you go, full housing setup for under $30000, but it would be a very low standard of living, but much nicer than sleeping in a car or on the street. In many populated counties it is illegal to sleep on your own land if you don't have an inspected house or utility hookups.