EDIT: Sorry for wall of text

I'd like to share my thoughts that came from experiencing homelessness myself for around a year. I'd like to split types of homeless people into groups but it's hard to do. Everyone has their own story, their own complications. Some things are similar, like being down on your luck or having addiction issues, but it really depends. Several homeless people that I knew back then are still homeless. Others come into and out of it on and off throughout their lives. Some people only experience it once. I'm really not sure of any exact numbers. I think there's projects out there that tackle that. Some shelters more than likely have that kind of data.

I think tackling the issue for real would require a pretty intense system change. Things we can do in the meantime are pretty much what you're calling traditional methods. The problem is that not everyone is taking each method seriously and not every method gets the amount of attention it needs.

At the end of the day, some people are unable to work or have a normal lifestyle. It might be because they can't hold a job because of their addiction, or can't because of other mental problems. In cases like this, we have to be able to determine who is who (because of limited resources I would imagine) and get those people the support they need to survive. Psychological, physical, etc...

One thing to realize is you probably won't ever be able to get all of those people on the streets to live a life that you consider normal. Some people are stuck in abnormal situations. Instead of trying to change that, we could instead come to terms with it in society, recognize that it's not really as bad as people think, get rid of the subjective norms that we have in our heads and create systems that take care of these people.

I'll give you an example. There's an organization in Des Moines called the Catholic Workers of DSM. They have a couple different houses each serving its own specific purpose. The volunteers there live an almost monk-like lifestyle. They gave up their possessions and basically get only what they need to survive. Sometimes the volunteers were actually once homeless people that eventually joined. They give away meals and clothes every day. They also do other sorts of work in the community. Instead of having the goal to get everyone a normal job and get everyone off the streets, we can set up a system that makes it safer, cleaner and healthier in general to live this lifestyle. That means some sort of housing, even if its extremely minimal, meals, fair treatment from the cops (in a lot of places cops can arrest you for being homeless and blame a variety of different laws), etc...

What I like about the Catholic Workers is they involve the people they help with their work. It's built for and by people in the struggle. It's maintained by the very people they help. In a sense, although they're not making a wage doing that work specifically, they have a job which is fulfilling and healthy.

Working with the homeless can be extremely challenging. You never know how stable someone is or how ready they are to do harm to get what they need to survive. I'm not trying to make homeless people look bad, but I'm telling you that while you're used to getting food out of the fridge when you need it, some people have been without food or sleep for a few days and their primal instincts are kicking in, so to speak. The reason why the Catholic Workers does so well is because they're in the struggle just like the people they're helping. They're familiar with their community, they know its people and they know what it's like.

The last thing I'll say is that just because you're not ending homelessness for everyone in one days of work, doesn't mean you're not making a tremendous impact in someones life by getting out there involved with the street teams and in other traditional methods. When I was in Memphis, I had a realization as I went to a nearby park to get food from a local church group that hands out meals regularly...Those people have been giving food for years. Sometimes no one even says thank you. They just get their meal and walk away. But the church group keeps coming out there and keeps working at it. If you really want to help people, at some point you have to realize that you can't do it all alone and you can't solve it in one swift blow. Anything and everything you do that is helpful makes an impact. Lifelong impact takes lifelong commitment.

You should get involved with a local organization, or several, learn what they do, learn the challenges they face daily and then ask them what they think the long term solutions are. You could learn a lot!