I'm positive there was a comprehensive thread discussion on here a couple years ago, probably worth digging up.
I'm also very interested in the subject. Personally, I think righties should be taught to shoot right. I suspect left-shooters whose parents handed them a stick to let nature run its course, weren't accounting for the fact that kids learn through imitation, in a lot of cases.
I also think the right hand is for power and aim, and the left hand is for balance. (Speaking strictly about right hand dominant people, of course).
Think about the legs and feet, and their role in all of this. It would be the same relationship. We need someone to watch left-shooting righties skate, to compile data on which foot they push off on, and also which foot they shoot off of. (First person that pops into my head as an example is Kessel. His shot is very deceptive, for this very reason.)