No, we just can't rely on them to explain everything! As you purport.
Only 33% of the homeless suffer from mental illness, and it certainly is not a strong predictor as to why rates are high in some cities but not others. That's the data.
> Affordability is a moot point for people in these categories
It matters to everyone, but even if we pretend it doesn't, that's 67% percent of the homeless.