If you have no idea how prevalent mental illness is in homeless people, and also its role as the single most important contributing cause, then you are commenting from a position of ignorance. Instead of devoting effort to virtue signaling you'd do better if you educated yourself on the problem.
If we go by these sources[1][2], homelessness is overwhelmingly an economic issue.
That's not to say mental illness isn't a contributing factor, just that the lynchpin into homelessness stems from economic factors, like insufficient income or lack of affordable housing.