Mostly because you have to bring people to those places and upgrade the infrastructure to support them there. Do the math yourself if you're unconvinced.

People in cheaper locations also fight back! Why is that location cheap and why do those people live there? Precisely because the density is so low and the community likes it the way it is. An influx of recently homeless people would be a huge disruption and no one would be happy with the change. Would you want to manage that situation? THINK!