Let's remember that mental health care is not as easy as a magic pill. It can take months to stabilize someone. Someone with schizophrenia may have difficulty staying on a regimen. (The side effects are bad in many cases, and the drugs aren't a magic cure.) Some people would do best in a psychiatric ward more permanently, for example, but that's including housing.

Bipolar treatment can stop working and it can take months to get things readjusted.

Inversely, homelessness exacerbates mental illness in many ways, and stabilizing the housing situation goes a long way toward stabilizing the mental illness.