Has this been tried? Create a non-profit (coop perhaps?) company that owns a residential building and rents at something akin to market rates or near it, but continually invests any profit into producing additional housing?
In LA for example, you can never get a rent controlled rent back to market. If someone is paying $600 for a 1 bedroom you're never going to catch back up to $1800.
All that said, I don't know why it has to be non profit. What you described is a just a real estate developer. Zoning is a more limiting factor than anything else.
In other words the $600 rent controlled apartment is a myth.
By staying near market rates you’re not “lottery winning” some people. By reinvesting all profit into additional units, you’re going to slowly drive the costs down.
0: https://www.lowimpact.org/categories/economy/housing-commons...