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.
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.
In other words the $600 rent controlled apartment is a myth.
0: https://www.lowimpact.org/categories/economy/housing-commons...