You're acting like 'housing them' isn't something people have tried over and over. It's super obvious. It doesn't work.
Well, it does work, I mean it does provide protection from the weather. However, you can't trust random people with access to something without supervision, because many will completely destroy it. You can't provide personal supervision to each person so that they can have a private space, because that would cost an incredible amount of money. Finally you can offer some kind of barracks/homeless shelter environment where you have an open space that is easy to supervise to the level of preventing arson and other overt destructive acts. HOWEVER, this means bringing together a bunch of homeless people in one space, and you can't provide enough supervision to prevent them from victimizing each other. Read up on the topic, time and time again homeless people will say that the most dangerous thing about being homeless is you have no protection from the other homeless people.
So on a more personal level, do you really think that super, super obvious ideas haven't been thought of before, and the world just needs someone like you to swoop in and say 'give them shelter!'?