Kekd.
It doesn't work for the simple reason that if you don't have enough homes, no matter how you shuffle people around and divide costs, someone is going to get the short end of the stick in some way. There are many places with elaborate systems of rent control and social housing, usually the effect is waiting lines and discrimination.
Yes, having to pay a lot for rent sucks, but you know what sucks even more? Applying for social housing and then being told that you should've started thinking of such things at the age of 4, now it's too late. That's how the Netherlands functions, despite having the highest ratio of government housing in Europe.