While I'll agree that for the vast majority of homeless that is the case, however, there are always those few cases where they ended up homeless for other reasons. For example, those who go bankrupt due to the medical expenses that they accumulated as a result of a sick spouse, and they have a limited fixed income.
Every major city, and even most minor ones, have resources to help homeless people, if they WANT that help. The problem is that the homeless don't want to abide by the rules of these shelters - no drugs, no alcohol, no cohabitation with a sexual partner, no criminal activity, etc. - and therefore, of their OWN volition, can't stay there. In other words, they make the conscious choice to stay on the streets.
I've been tangentially involved with enough charity shelter organizations to know what the reality is. Drugs is the main problem. And there are loads of programs to help these people get off drugs, IF they want it.