Well, of course you are right that everyone can't be a teacher. However, realistically, I think we are very much on the opposite end of number-of-great-people-who-are-teachers spectrum.

Also worth pointing out that this isn't necessarily true for secondary education - Universities are institutions which allow great teachers to both do great work and teach. I'd hypothesize that if the same were extended to other institutions, and also to younger students, much value would come of it.