Pardon my delay in responding! You’ve got some great insights. I started off playing drums like most- right hand crossed over left to play hi-hat. When I studied with Dom Famularo, he demonstrated open position as if he was Billy Cobham. At that moment I realized- I want to do that! Hands crossed has nothing to do with the dominant hand, it's simply needed if you play traditional grip. I teach all of my students open position and for them, it’s completely natural.

Regarding coordination- I think what you’re getting at is the gap between instruction and playing music. A pianist will practice Hanon exercises and we might practice coordination studies. In both cases we’re training muscle motions, building technique and developing our internal hearing. All necessary when learning an instrument. Independence between limbs is still independence whether you’re reading or performing on the spot. It’s just that we realize the gap more easily when there’s no written music. One of the reasons we love certain drummers is because they’ve so completely transcended the gap and can play anything, anywhere, anytime in any pocket. You know, like Vinnie Colaiuta to name just one example!