I still wonder why more of that wisdom doesn't reside in the catcher, and whether it could be spread around.
I think some of the "wisdom" you're talking about is available only via what they commonly refer to as instinct. It's in all kinds of sports -- some players "see" stuff that other players don't, recognize situations faster, avoid mistakes much more easily. When they say someone just "knows how to play/pitch," I think a lot of what they're saying is that the player has good instincts. It's nebulous, and it's not teachable -- but it's real.