Songs about madness were seen as an English specialty in the 18th century. Matthew Lewis's "Crazy Jane" (tune: Fy gar rub her o'er with straw) is from the end of that period. Stereotypical - woman goes mad after being abandoned by a lover.

The problem with making a more realistic song about psychosis is that you want a song to have a meaningful story, and madness is not meaningful. The sort of delusions and muddled thoughts schizophrenics suffer from don't go anywhere - they just make normal life impossible. And the emotional extremes of bipolar disorder don't emerge from real-world situations with any sort of logic.

I could imagine a song about having to deal with madness in a loved one, though - like what "The Dutchman" does with dementia.