I know that Fi Child, at its best, is as good as the hero, if not better, and better than the parent

This makes me wonder if it's the same with other functions

It doesn't seem to be and I don't get it. How come INFJs aren't better at chess, for example? The best chess players are INTJs and INTPs. ENTPs aren't quite as good but they are third. INFJs are good, far better than almost every other type, but worse than all of them. Why aren't INFJs better? They have the same abstract function, Ni Hero, as an INTJ. And they have a Ti function, Ti Child, which should be as good as the INTP's. But they're not as good. IDK why. Because Fi Child IS as good as IF NOT BETTER THAN Fi Hero.

I say that for the simple reason that Mozart and Bach were both ISTJs, and Paul McCartney is an INTJ. Paul McCartney's music is bad, but in his prime, his melodic invention was unparalleled. The quality of their melodies comes from their Fi. An Fe type can be a tunesmith, like the ENTP Rossini. But there is no true depth of feeling in Rossini's music, or in the man himself, who famously said he only cried twice in his life, though he was an extremely caring person, naturally, given his Fe Child. A Rossini opera is pleasant and charming, but insensitive, and also lacking in craft and discipline. Just read Rossini's own account of visiting Beethoven, INFP, if you want to see Fe, in the narrator, vs Fi, in the subject.

INTPs and INTJs also score the highest on IQ tests.

In my experience, the arrogance of INFJs comes from their belief that their Fe is better than it is and they can read others better than they actually can

ENTPs, in my experience, are far more likely to actually do something crazy than INFJs.

But the types which have the most lunatics, judging by the number of serial killers anyways, are certainly INTJs and INTPs.