So you would be willing to extend a modicum of human compassion only if a larger percentage of the population create crime and filth? 
A 10 minute google search about who the homeless are and whether or not they have freely chosen homelessness, are they addicts, etc. would word you up on how wrong you are. 
I agree that we need to change the way we think about the homeless. But simply making them disappear from the view of upright folk, as you suggest, is not any kind of answer. The compassionate and cost-effective way is to give them a home. But you apparently prefer to spend more for less.