That would be something interesting to watch and see why that works for you. Really you want to build your skill set so that you can shoot and move in any direction effectively. That being said I usually shoot better on the move when backing up, mostly because you land each foot on your toes instead of the heels and this absorbs the impact a bit better. I've tried moving forward by using the toes, essientially tip toeing, but it doesn't feel natural and you can't roll through the step so you tend to bouce more.
I'm guessing you use a Weaver type stance which blades the torso which would make it difficult to move and shoot straight ahead as you have to unblade your torso but the bent left arm fights this position.
In both these picture you can see with both arms slightly bent I can engage targets either straight ahead or to the side while moving at a brisk pace.