You don't really save all that much money by building a barely livable pod vs an actual apartment. The big cost items are kitchens and bathrooms. Those are mostly fixed costs, i.e. it costs the same to plumb a toilet, shower, and sink in a 50 sq foot bathroom as a 100 sq foot one. Only when you get to stupid high real estate cost does a ~300 sq foot pod start making sense over ~600 ft 1 bed or ~1000 sq ft 2 beds.

It's a bit counter intuitive, but the best way to lower the cost of housing for the poor is to build more housing for the upper middle class and up. They will trade up houses which will increase the supply of used houses driving down their price. It's essentially impossible to build something new that will be cost competitive with something that already exists.