Mental illness is unavoidably inextricable from culture. There’s two classic determinants of human behavior, nature and nurture. Nature generally refers to DNA. Nurture refers to things like culture, upbringing, environment.
Both of these things are highly informed by how we think about them at the time. To call Caligula mentally ill by the standards of psychiatry that we have now is to profoundly misunderstand both history and Caligula. Rather than to try to understand history and Caligula, you’re trying to reify your own morality and views onto history.
It’s easy to get misled by the illusion of the reproducibility of science. But things like psychosis had very different implications back in Roman times than they did today. For one, family and community dynamics were much, much stronger than they are now. Someone with classic schizophrenia might well have not been totally ostracized by his community and instead been looked at as a font of wisdom.
Trying to understand history with current frames of thought only does the opposite.