You are making something of an induced demand argument that basic services for people who can't care for themselves will generate more such people. Fortunately, most people of sound mind understand that living in a former Motel 6 is not a good life and in practice the number of people who are "incentivized" by it are much less than the number of people taken off the streets by shelter. That's why cities with robust shelter programs like Houston have far fewer unsheltered homeless people.