Affordable housing is little better than the drinking fountains for colored people from years past. You don't build affordable housing. You build housing and then prices decrease from the increase in supply. If you're feeling extra bold, you build dense housing to massively increase the supply.
This is kind of true, but misses an important point. Builders won't increase the supply if unit price is close to unit cost as their profit would be narrowed. This is to say, if materials, labor etc is expensive, affordable housing may not be affordable either.
Sounds a lot like the reasoning behind farm subsidies, doesn't it?