> The only real difference between a mentally ill homeless person and a normal mentally ill person is the home. Why wouldn't a stable home be the answer?

if the mental illness is as serious as schizophrenia, a home isn't enough. The issue isn't just about the mentally ill person's welfare, but also if that person poses a danger to others who live nearby. There is a strong correlation between schizophrenia and violent crime. Without treatment in a controlled environment like a mental hospital, it's hard to see a mentally ill homeless person being able to safely integrate with society when they also lack a family and friends support network.

> I was his primary caregiver, fair or not, and his doctor didn't want him living alone for his own protection.

This is the issue. The homeless will not have the luxury of having a caregiver to be able to live independently at least initially. I'm sure why it's so hard for people to accept that the homeless people, who also have mental issues, just don't have access to the same resources that a non-homeless person with mental issues has access to.