We are not attracting them, nor are we supporting them in any but the most minimal way -- unfortunately. Every city in the US has homeless people. The number is increasing because it is getting harder to find living wage jobs, affordable housing is decreasing, and rents are increasing. We have created an economy that is hostile to working-class people.

As for increasing the number of killers, you could make the same argument about increasing the number of housed, which is also happening. I don't have any evidence that homeless people are more violent than the housed, and until I see such evidence I don't believe it. 

This whole idea is just a distraction. The real issue is that people need shelter.