I'm just wondering why we automatically refer to any hand as playing strong hand, seems if we teach confidence and teach to expect independence from the beginning it would help up and comers greatly.
I think you just answered your own question here. Many drummers were taught to play crossing the right hand over to reach the hi-hat, myself included. When I was 10 and taking lessons, I didn't have the foresight to question my teacher about his methodology, I simply did what he told me to do.
Seeing drummers like Simon Phillips, Lenny White, Carter Beauford, etc..., who can play open-handed or with no "strong" hand makes me really jealous, because I'm sooooooo right hand dominant.
On the plus side, exposure to those drummers and more have given me, and probably countless other drummers one more excuse to work on developing new techniques (and getting new gear!).
If I were to take lessons again (which I hope to do when I find a qualified teacher in my area), I would want this concept to be a significant portion of the instruction.
Similarly, teachers today should probably be prepared to take their students in this direction; expecting independence as the rule and not the exception, and encouraging students to use the approach that's the most comfortable for them.