You are absolutely correct on all points. I can say this with such certainty because I have direct experience having lived that life in multiple cities in five U.S. States.
Though my reason for choosing this miserable route was atypical, it was still my choice and led me to one, unwavering conclusion: the vast majority (80%) of the American homeless population exists as such by choice.
The items up for barter were a life of conventional stability created and sustained by employment and a shambled ghost of the same created by, and serving only, the constant use of addictive substances.
Futhermore, even if this majority were provided a "life" complete with all associated components such as house, car, clothing, etc., AND devoid of any financial obligations thus related, they would squander ALL of it and return to destitution within six months.
Even the inclusion of an unlimited supply of the subject's chemical of choice would only add an alternate method of property abandonment: death from OD.
Of the remaining 20% easily half possess some form of mental illness that degrades or completely prevents normal social existence. Few in this category receive treatment of any type, many to the very real and gravely serious endangerment of society at large.
Of the final tenth, 8% of the total, can be deemed "other." Even though their social circumstance was not dictacted by addiction and/or mental illness they are still willfully embedded within the homeless communtity, usually to such an extent as to be indistinguishable by any standard. Again, by clear and willful choice.
This leaves a paltry 2% that have had homelessness abruptly thrust upon them. The common theme shared by this subset is, simply put, loss. Be the lost item(s) a person, place or thing is of little importance. What matters most is the significance attached to it by the one now without. Removal of something held near and dear creates a void in the soul proportionate to the item's perceived value. If the item is deemed life-critical then its loss can be devastating and life rendered thus moot and unworthy of effort. Essentially, this is the death of the soul. Though the vessel appears whole it is empty and thus beyond ruin.
Once life's functional components are abandoned, its a quick journey from checking one's mailbox after coming home from work and a park bench bedroom or homeless shelter.
When material loss is the catalyst for homelessness, most actually recover and move on.
But, if what's lost was near and dear, the recovery rate is substantially lower. In fact, most in this category do NOT recover, instead allowing themselves, as individuals, to melt into the dismal mass of the homeless body whole.
As stated, all information presented above is sourced only by my direct observation and exerience and, as such, is merely opinion.
Take it as you will.