It’s not a one size fits all decision. Some are so strongly cross dominant they can’t function and on the other extreme they may only be able to notice it when carefully tested with the finger in the eye test. Along the same lines not everyone can be ambidextrous.
I’m left eye dominant and right handed, but there’s no way I’d want to switch, and I’m 90% ambidextrous from working residential construction. For over a decade, heck two decades, I’ve forced myself to practice swinging a hammer left handed at least little bit on almost a daily basis, but the muscle control will never be as good. Carpenters read tape measures all day and while I naturally line up my left eye, it’s no harder if the angle makes reading it lined up with the right more convent.
I shoot just fine, despite warnings as a kid I would struggle with a shotgun or pistol, which never materialized. I may never be an Olympic skeet shooter, which doesn’t bother me since I hit clay targets just fine. Judging by the number of Olympic smallbore and pistol shooters with a left eye patch, many of them have cross eye dominance issues they’ve overcome quite nicely. Closing the off eye is a fact of life that came natural to me, but it doesn’t seem like a hard to understand thing to teach kids. I see parents getting on their kids for closing an eye and they are just making it harder than it needs to be since those kids have already figured out what they need to do.
Anything is easier with practice. I shot thousands of rounds a year through a scoped pellet gun before my first 22 and did the same with it before any center fires. The biggest issue shooting a 22 pistol was adults trying to force me to keep both eyes open. When I finally had a need to fire off a bench at a formal range closing the off eye was natural, even though well meaning adults kept trying to force me to leave both eyes open. As little as kids seem to shoot today it’s a wonder they can even learn to hold it correctly with heir strong side, let alone forcing them to throw a baseball left handed. If you’re right handed try swinging a hammer or throwing a ball as a lefty, then try closing your left eye and tell us which was easier.
When shooting rifle, pistol, shotgun, or bow it’s natural to keep both eyes open until no more than a half second before lining up for the shot, so the supposed lack of field of view from closing the eye is a nothing burger for me and many eye closers. For quick snap shooting with the rifle/pistol/shotgun ready at waist level the eye doesn’t start to close until 3/4 the way up, maybe 1/4 second before needing the eye to be lined up. As soon as the shot is off the eye naturally opens. Easy peazy.
The other thought that it causes too much eye lid strain is also a nothing burger for shooting or spotting scope use. In fact just now seeing which eye is easier to close while typing this, closing the left eye is not only easier from muscle memory, but automatic. If I were to wink at the wife it would be my left eye.
I’ll never say someone should copy me, because we’re all different so do what works and don’t try to force what doesn’t. Turning a kid loose with a pellet gun and unlimited pellets will eventually show what works best.