The words core stability are being thrown around quite a bit in this thread. I am curious as to what this means? What is she stabilizing and why? What specific quality of stability is she trying to improve in this drill? For me, the key is Marc's comment, "Increased body control and stability", but what specifically does that mean?
I am inclined to describe this as an isolation exercise. Essentially, she has become a legless pitcher. She is forced to open and close with her core without using her legs to step open and/or externally-internally rotating her legs. She is also forced to control the amount of rotation. If she rotates too open she falls off the ball, if she closes too much she falls off the ball. This requires her to try and maximize the amount of rotational energy transference within a small range of motion and coordinate that action to her arm circle. This would likely lead to a quicker and more forceful opening and closing within a controlled ROM. I am inclined to believe that isolating such feelings for a few sets and then applying that feeling to a normal set of pitching might have some benefit.
I am inclined to describe this as an isolation exercise. Essentially, she has become a legless pitcher. She is forced to open and close with her core without using her legs to step open and/or externally-internally rotating her legs. She is also forced to control the amount of rotation. If she rotates too open she falls off the ball, if she closes too much she falls off the ball. This requires her to try and maximize the amount of rotational energy transference within a small range of motion and coordinate that action to her arm circle. This would likely lead to a quicker and more forceful opening and closing within a controlled ROM. I am inclined to believe that isolating such feelings for a few sets and then applying that feeling to a normal set of pitching might have some benefit.
I can see broken wrist, arm, finger all over this exercise. 
