He's "good at programming" like Galileo was "good with telescopes." Computers, telescopes, hammers, they're all just tools, and Carmack has proven himself as far more than just a handyman.
He's the kind of person where, if you show him what you're working on and he doesn't understand it, you probably need to go back to the drawing board.
Cult of personality much? Don't get me wrong, Carmack is one of a kind. But seriously, "if Carmack doesn't understand your idea => your idea is hopeless" -- this can not be healthy.
EDIT: I'll elaborate a bit. In my experience in both industry and academia I've witnessed numerous occasions when brilliant people would get things wrong, ignore a brilliant idea, follow a hopeless research direction, etc. etc. Authority matters, but _nobody_ is flawless.
Your argument is a bit like: here is this amazing long-distance runner who trains for years at a time, had he put all that effort into painting he would be a new Picasso.
For what is worth computers are unique tools unlike any other tool that mankind has invented before - thus it is much harder to tell what other jobs would a good programmer excel at.
He's the kind of person where, if you show him what you're working on and he doesn't understand it, you probably need to go back to the drawing board.