I'm not sure, but it would seem to me that shooting both eyes open requires you to be dominant in 1 eye and the greater your eye dominance, then the easier it is to master this technique.
I think that pgdion has a good point there. For me it was training that got me past the difficult part of using both eyes when shooting. I'm at the point now that I can switch eyes and switch hands easily including being cross dominate.
For me it’s the larger field of vision and better depth perception that shooting with both open makes it worth training for.
Training turned out to be very easy. It was suggested by a good friend that used to ride trains with Harry Truman. Take a cheap pair of sun glasses and tape over one side. This allows you to keep the weak eye open and will help from squinting and at the same time allows a clear view of the sights.
From his suggestion and after several hundred rounds I took off the glasses and I found it easy to keep both open and easy to center the strong eye on the sights. I have been doing that for the past 30 years.
Try it yourself, take an unloaded gun and hold it up with one hand and keep both eyes open. You will see a double set of rear or front sights. Then just bring your weak hand in front of your weak eye, you don’t need to cover it, just block the sights. The sights will easily align without squinting or closing the weak eye.
For me where it really helps is with eye fatigue and also scopes like Aimpoint’s.
Personally I don’t think that it’s impossible for everyone, but it can take some training and practice. But I do feel that being able to shoot with both eyes open will make you a better shooter.