City-owned housing works great here in Vienna. The City owns like somthing like 20% of all apartments and rents them out at basically non-profit rates. It works fantastically! It does not only offer lower rents, but it makes people realize that landlords often charge unnecessarily high prices and makes people demand better from landlords, so these lower their prices as well to compete with the city apartments.

Edit: for reference, i'm paying 500€/month (roughly $600/month) on rent and it's already a private-owned apartment. In the city apartments, the rent is even lower still.