In Linz we have something called "housing cooperatives" (the German word is "Wohngenossenschaften"). These cooperatives build apartments, and to rent them you become a member of the cooperative. The goal of these cooperatives is not to make a profit, but to provide affordable housing.
And it's amazing how well that works! Rents are typically 50% lower than average, and the buildings are always well maintained. In general, they also have better amenities (playgrounds for children etc) compared to privately owned apartment buildings. The only problem is that there are very long waiting lists (more than 5 years in some cases).
It's amazing how cheap good housing can be when it's not necessary to make a profit for the owner.