If it's a clicky scroll wheel it would be useful mainly for things like that, but if it's analogue then it could give you some fairly fine control over movement in game as well - it's the kind of thing that you could maybe assign as "tweaking" movement control in something like a flight game, letting you make the gross movements with the thumbsticks and fine adjustments with the shoulder wheels.
You could also use it for other things to do with character control - instead of mapping "dodge" as a digital button that gives you a single dodge move, why not map it to a shoulder wheel and give you control over the speed/direction of the dodge? Or you could use it as a "rewind" in a time-control platformer to give you intuitive control over the speed of a rewind to get you back to the precise moment you wanted. There are probably plenty of other uses beyond simple menu control, and having it at your fingertips when you're holding the controller makes it natural to do.