@Chickadoo There's fairly regularly threads on MN from posters who are at risk of or are homeless. None chose it.
Many are working, many have children, others are ill or disabled or caring for a disabled child or elderly parent (but not unable to keep a home and the issue is simply the low income of benefits).
These posters have been asked to leave by their current landlord on a "no fault" eviction, or the rent has been increased to unaffordable level. Or they've fled DV.
You're right that they're struggling to keep a home. You're wrong that it's because of being mentally incapable of that. It's because they're on low wages or benefits - and housing has become unaffordable for many families and individuals.
Single women (both with and without children) are particularly affected, as per the link I posted upthread.
Yes, separately there are some people with mental health issues that mean they struggle to keep a home. As I've said, they need genuine supported housing - with 24/7 resident trained expert staff. As others have pointed out, these people have generally suffered immense trauma and/or are very unwell - and need appropriate help.
However it's a myth that the latter group make up the majority of homeless people. Perhaps in the past, I don't know, when there was more social housing available and full housing benefit, but things change.
No idea why some people cling to the myth. It's very obvious that if there's a shortage of social housing and private landlords wanting certain multiples of income from prospective tenants, loads of people on lower incomes risk being homeless.
It's really that simple. And even if there really are a small minority who really do choose to be homeless, we can still address the majority who don't - by providing more social housing (and where relevant, proper support).