Stances are great for initial learning of trigger control and other fundamentals. Stances can also facilitate accuracy and follow-up speed in certain conditions. However, as others have noted, stances may not always be suitable for conditions.
That said, training in trigger control, sight alignment, point shooting, etc can all be put together in different ways.
In my dojo, one aikido instructor occasionally likes to have us execute throws and techniques while balancing on one foot. This is not something one would deliberately do in a hand to hand scenario, but as a training exercise, to prove that one can control one's center while in weird positions, it is pretty interesting.
So, to see if this would translate to shooting, I decided to try something odd today while breaking in a new Kahr MK9. The following group isn't great for 5 yards, but it's not bad - considering it was shot with my left (weak) hand, while balancing on my left foot, and firing from a flash front-sight picture:
That said, the shooting fundamentals involved were primarily derived while shooting from more formal stances, and the balance involved was from training in MA and some yoga.
Going back to my earlier post, developing balance is useful in lots of ways; keeping knees slightly flexed, and weight on the balls of the feet, is also useful for many applications.