Of course shooting pretty good with one eye closed is far better than shooting poorly with both eyes open.
But, according to a lot of trainers, it does become important in a high stress situation like defending yourself, because you will almost certainly not take your focus off the attacker, close one eye, refocus on your front sight, get your sight picture and then take your shot. You will most likely point and shoot. Without practicing with both eyes open, and practicing quick target acquisition your shots can be way way off. That made sense to me so I practice that way often.
A lot of practice can be done at home to help. At least for me it did. (insert safety disclaimer here). Pick a 'target' at the appropriate distance, start at a low ready position, quickly bring your gun on target, hold it, then close one eye and check your point of aim. repeat repeat repeat. You should start getting closer and closer to the correct point. Then practice the same at the range with live fire. I was practicing this just Monday. (B.B. may have noticed)
If you are consistently far off to the right or left you may have a cross dominance issue. Not hard to accommodate but that's a different story.