Not looking at this from an ethical perspective, but, I think if you refined your question to say that you only want to annihilate homeless people....
lol, just playing devil's advocate here
#1 economically speaking if we removed all homeless/unemployed people or a good portion of them, it would likely result in vaulting our employment rate to unprecedented levels and it would also relieve a huge tax burden off of area of law enforcement, education, and social benefits like medicare, etc. It could also revive certain areas of downtown districts and bring new life to cities.
What are the negatives? Well not from an ethical standpoint, I can't think of much....
Probably just the cost of annihilating them would be expensive in its own, you would have to dispose of the bodies and also the cost of how you kill them. Edge blades would be most efficient, anything more then that would cost too much initially and it would take years to see the payback.
This won't remove crime or trailer parks though, since those people still contribute to society