Well, in MY own opinion, and legion don't come after me with guns as u usually do, i think that the fact that one does not see any homeless people IS a result of a better welfare system.
However there are exceptions.
Here in the UK the amount of homeless people who actually sleep on the street is quite high. Sadly those people are the first ones to choose to do it. My Ex used to be a manager in a hostel for the Shaftsbury Society (the biggest catholic charity organization in Britain) and really, u'd be surprised how many guys actually refuse the free accommodation and food they are entitled to, in order to go back to the streets...
So it's not always a welfare-system issue