Maybe it would be easier to learn how to shoot left handed. Your eye dominance is reinforced all day/every day. Shouldering a long gun is a single-application motion.
Yeah, learning to shoot left-handed is the best solution, except that most guns are made for right-handed people. Autoloaders tend to eject in front of you when you shoot left-handed unless you have a left-handed gun, which is rare and generally more expensive. I think shotgunners are especially distracted if multiple targets are flying like skeet.
Good point. You see handguns with an ambidextrous safety and/or mag release, but I never thought of the casings flying in your face.
Another thing I always had trouble with was single lens microscopes. In school they told us to always keep both eyes open to avoid eye strain. I always used my right eye to look through the lens just because I adjusted the focus with the right hand. It was hard to not see what the dominant left eye was seeing (the table), so I ignored them. They never said anything about dominant eyes back then.
You get the same recommendation for shooting...even using a scope. I've not shot enough with a scope to have a strong opinion, although it sounds confusing to me. I cannot imagine any schoolkid using a single lens microscope and not closing one eye. In the shooting scenario, the idea is that you gather info regarding the surroundings,which may be of some value. But as you said, why look at the countertop? If I recall correctly, the idea is to reduce eye strain. Processing irrelevant data seems distracting to me.
Some people can view through a single lens and draw with the other hand and eye what they see. I could never master it, but I am not any kind of artist.
When I first shot a rifle, it was at a range and the guy next to me brought in his paper target which I was apparently shooting too.