While yes it is cheaper in some ways, the problem is people will be less likely to be creative or lean on personal support networks (i.e couch surfing, live with family, etc) if the government through the taxpayer will just hand you a key to an apartment no questions asked....
There were a couple of times we were technically homeless as a child, I slept many nights on the floor of my grandparents home, or an uncle, etc. so I am not unsympathetic to being in this condition. However I also do not believe government handouts are a solution to the problem
I believe in Handups, but not handouts.