suggestion

Well we don’t earn that much so this would very fast end up with poor people 

This takes away from the ability to create their own home and hinders where they can live. At the current moment, graduates can live just about anywhere they wish (within realism and reason). One of my own graduates lives in Japan.
If we could only rent/buy the homes available, I highly doubt any of them would make sense to fit in with Japanese culture. 

Without this feature, they may have houses based on their own preferences and the area they live in.