It does not seem like a stretch to expand the definition of mental illness to include mental conditions which predispose to the commission of violent crimes. Certainly such conditions are maladaptive for the sufferer.

I meant mental health, I didn't mean mentally ill. Mental health even includes being unhappy.

Not sure if violent acts are entirely random, I have not enough expertise on that. Currently I assume most acts of violence are not entirely random; and if they are, they are a mental/medical/neurological illness. And it might be perfectly normal to be dispositioned to be like this, but it would still be a problem.