> Be coming homeless isn't a problem with the person, it's an outcome of the system we live in.
Like most things in life, I don't think it's as simple as that. I think it's a complex mishmash of systemic factors and individual choices that cohere into a big ball of suffering.
For example, I had a close family member who was an alcoholic. He couldn't keep a job because of his drinking problem, and wound up going through all his friends and family who would take him in (before wearing out his welcome at each place in turn). He was getting put out of the last place he had available, basically, when he died suddenly. But if he hadn't died he would've been homeless. Was this a problem with the system? Maybe - he had a pretty good support network, but you could make a decent case that if we had the right support system in place at the right time it would've helped him. But also, there was absolutely an element of choice to it. I have a lot of sympathy for the guy, because addiction is a bitch. But systems of life or no, he made choices at various points that led him to the point of homelessness. A different person in the same circumstances very well might have had a different ending to their story.
I don't think blaming the homeless is productive, certainly. Their lives are shit and they don't need someone smugly telling them "just do better bro". So I do think that trying to improve the system we live in is just about all we can do (that, and be compassionate to people we meet). But unfortunately I also think it's not realistic to expect any amount of systemic change to be able to solve the problem.
The population of homeless people would end up probably where it was when you killed them all. Though I do wonder how long that would take