No doubt, 'the poor protect the wealthy in this world' (from the music of The Devine Comedy and possibly older origin). Criminality has its roots in the wealthy controlling the poor, look back a few hundred years in Britain and if you were starving and stole some food, you were executed, or as times became more 'enlightened' deported to Australia. From the laws perspective its better to starve than to steal. Some homeless people want to be housed, others I think really have become so accustomed to living on the streets that they dont want to change, that is their choice.
I however do feel in your post you dont really propose any more workable solution, what do we do with serial murderers, rapists and so on, ask them to stop?