I have always subscribed to the theory that we were given 2 eyes for a reason.
I don't think we were designed to do anything with one eye closed, especially things that involve balance and hand eye coordination.
Now throw in hand eye coordination and balance and possibly uneven footing, maybe 25 feet in the air and stress and I want as many eyes working as God gave me.

Just try standing still with one eye closed for any period of time and see what your body thinks of that. I just think that learning to shoot with one eye closed will have a negative impact on a persons inherent shooting ability.

Eye dominance issues can be worked on by squinting down slightly on the dominant off eye to take it out of play but I would never close it entirely.