> Mental health is partially (largely?) a function of physical health.

If only that were true, then the answer for every mental problem would be 'exercise'.

Not saying that people with mental health issues wouldn't benefit from exercise in general, but that goes for everybody, not just for them.

And even if their mental state would improve I'd be surprised to see 'schizophrenia cured by exercise' as a headline. And the same would go for plenty of other mental health issues. Mental health is influenced by physical health to some extent but to claim it is a function of physical health is a step too far I think. You can have perfectly healthy people with a very bad mental make-up and vice versa.