That might be confusing cause and effect. It's not that homeless people are more likely to be mentally ill, it's that the mentally ill are often homeless. And

That might be confusing cause and effect. It's not that homeless people are more likely to be mentally ill, it's that the mentally ill are often homeless. And that's by choice - we've decided that we'd rather not give a shit about mentally ill people, because it might cost money. (Cf. the killing of the Mental Health Systems Act)