The largest reason for homelessness is addiction.
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> that homeless people nearly universally choose that lifestyle,
I'm sorry but I can't really let that slide. A lot of homeless people aren't homeless because they chose that lifestyle and your anecdote doesn't change that fact. A lot of homeless people (roughly half of them) have serious psychological issues that make them barely able to function normally in society, this is why a significant number of war veterans are homeless. Don't make me started on people of all sorts or people that are unable to have a home because of their history (former criminals, illegal aliens, ...).
https://www.bbrfoundation.org/blog/homelessness-and-mental-i...
Few people would chose that lifestyle willingly, certainly not "universally".
I slept rough 2 times in my life, in dangerous places, and it was already bad, I can't imagine having to do that for months or years.
My experience living in a city with a non-trivial homeless population is most homeless -- at least the visible ones -- are predominantly able-body young men (and increasing women too) in their 20-30s. We're not talking factory workers who got laid off after 15 years due to outsourcing. They strike me more like urban, drug addled version of Chris McCandless from 'into the wild'.
Of course this experience may not reflect other regions.