I think society doesn’t want to face the fact that many people in poverty are a job loss/illness/accident away from being homeless. So, society makes it into either a moral failing (avoidable) by blaming drink/drugs or into being mad (which most “respectable” people think can’t happen to them).
I didn't want to copy paste the whole of your post but everything single thing you wrote is exactly right. You've articulated what I wanted to say far far better than I ever could.
Many, many people are on low incomes through no fault of their own. Illness (physical or mental) is a common reason. Housing benefit/UC simply doesn't cover many rents. Even when it does, increasing numbers of landlords don't take tenants on benefits (including those in work needing top up benefits). This is how people become homeless. Getting sick, being made redundant, DV.
A PP suggested street homeless women are likely those unable to maintain social relationships who pick bad boyfriends. Presumably true for some (and they should be in supported housing rather than left on the streets), but there are many more like me. I'm not (yet) homeless but could be if I left my violent partner. Which he knows. It's one of the ways he controls me.
I was/am very social, had good friendships and work contacts. DV destroys your support networks. Financial abuse, emotional abuse, coercive control, hiding bruises. Also, they don't present as terrible boyfriends at the start. You don't realise until it's too late.
I have chronic health conditions. Easily managed but my partner makes it difficult to do so. Being ill, even without DV, isolates you. When an ongoing health condition stops you getting out and about and you have to cancel meetups or not say yes in the first place, friends start to drift away. Family are very elderly and looking at care homes. Siblings both live abroad. Abusive partner has slowly cut me off from work and friends.
This is how some women (and men) become homeless.