My take is that we use the sights to 'train in' or build muscle memory. We fire shots to confirm that our sight alignment, sight picture, and trigger control are adaquate for the target/distance involved. This allows us to focus on the situation as it unfolds, and to verify the sight picture/sight alignment as we press the trigger once we make the decision shots are needed. The greater the practice, the better the outcome. This is why much training can be accomplished without fireing shots. Also, why shooting (hitting)while moving must be practiced.
Once the shooter has mastered the basics (usually shown by shooting groups), the other elements can be brought into the mix. Stance, refined sight picture, etc. are all means to obtain the end of hits on target. Stances have evolved to speed up the learning process, and are used because they work well for most people.
Illustration: A new Agent came to our office, and I took him to the range to qualify. On the shoot signal, he turned 90 degrees to the line of fire, dropped into a deep crouch, and fired one handed. He did this at all ranges back to 25 yards. He completed the course, turned to me and asked what I thought. He had cut the center out of the target. He commented that, while he was living in Alaska, he taught himself to shoot. I looked at his target, and said "Don, don't change a thing."
I would not teach that stance to anyone, but it worked, and worked well, for him. If it works, don't fix it!