Psychiatric research and article are known to use statistics on schizophrenics, and to be citing that in the homeless population many people have been diagnosed with schizophrenia, to a rate of about 45% of homeless people. A psychiatrist wrote that in his site, without mentioning if this is global or national rate of schizophrenia in homelessness, but never mind that. That point is, when there's a much more preferable, much less subjective, much less contrived theory, one should drop one theory for the better theory, as is the case of cognitive science and IQ. The incidence of both homelessness and schizophrenia together can be both linked very reliably with LOWER IQ, or LOW IQ scores.
Arguably people with lower IQ have worse reasoning abilities, inferior problem-solving abilities, and overall severe difficulties adjusting to civilization's reality. The relationship between the three variable[*] can be tricky, but it's quite possible that IQ explains both and has direct and indirect effects on outcomes, and inequality. IQ here presumably underlies all cognition, and all cognitive functions in humans. We can of course claim that a pink unicorn governs reality and all human outcomes, or find other logical explanations, or simply admit that IQ scores predicts life outcomes like homelessness, schizophrenia, and of course comorbidity between other life outcomes (even physical response to certain treatments!). So because both homelessness and schizophrenia have a cognitive source, the correlation between the two can be easily explained by checking IQ scores.
The problem is the ideals of the Enlightenment, which empathically emphasized human ability to over reality and gather knowledge. It's these ideals that gave rise to ludicrous claims in our technological age that science can solver everything, which it doesn't currently, but they did leave a black sheep in psychiatry.