Well, knock on wood, I'm not an X-eyed shooter. I'm a born, bred, and trained south paw. I do everything in life with my left hand, left leg/foot, and left eye. I can't even scratch my **** with my right hand. Well, I do play a right handed guitar, but I sure don't consider that being ambidextrous. It's just that I never had a left handed guitar .....
And while I certainly agree with you on practicing with both strong and weak hand shooting, that has little bearing on the subject of X-eyed shooting. The 'strong' hand is usually the same as the 'dominant' hand, and the dominant hand is the one you've learned to shoot proficiently with. Over many years of instructing, I have worked with many X-eyed shooters. It's been my experience and typically the recommendation of most instructors who deal with it (X-eyed shooter) that if I can start with them early enough in their shooting career, and I can convince them to shoot according to their dominant eye regardless of the dominant hand, they will eventually become naturally more proficient shooters. On the other hand, if they've already developed the habit of shooting X-eyed, it becomes a much harder task not only to help them become a better shot, it also becomes harder to convince them to shoot following their naturally dominant eye. Their shooting competency then becomes directly related more to how much they practice rather than taking advantage of any natural proficiency.
I myself also usually shoot open sighted handguns and long guns with both eyes open. Back when we were shooting a lot of Hunter's Pistol silhouette competitions, we used scopes of various kinds on our competition handguns and one eye was the norm. But with scopes you're actually focusing on the target anyway and involuntarily seeing the cross hairs. In fact most, if not all instructions for reflex sights today will recommend you focus on the target and not the red dot/window. If the red dot and open sights co-witness, you will involuntarily see the gun's sights even when focusing on the target.
I just recently put a SMSc red dot on my Hellcat, and the red dot sits directly on top of the front sight when shooting. It would be at approximately the 6
clock position on the target. The open sights and the red dot coincide at about the 27'-28' foot distance, just shy of 10 yds. And I love the 'ball-n-the-bucket' Hellcat sights because they are so easy to see even without focusing on them.