Mental illness and substance-abuse as well. So much of homelessness in America is a result of deinstitutionalization decades ago with no credible alternative put in place.
Exactly this. This program will probably help a lot of people down on their luck. Those kind of people utilize shelters and will generally do whatever they have to to get off the streets. The classic panhandling hobo however, is mostly incorrigible and nigh impossible to get on the right path. It takes a huge amount of intervention to get a chronic subtance abuser or schizophrenic to live independently.
I don't see how that fallacy can apply. We have pretty good definitions for chronically homeless. Here's a good summary, and there's a linked PDF with more data. Exhibit 2.7 in the PDF says that among the single homeless population (not families) 68% are substance abusers and 48% are mentally ill.