I like this definition of the purpose of coaching from the Management Craft blog.

Coaching in a business setting has four purposes:

1. Coaching should improve client coachability.
2. Coaching should help the client get unstuck and moving toward his or her goals again.
3. Coaching should enhance client self-awareness.
4. Coaching should facilitate breakthroughs.

That last one seems to be the real purpose in my mind. If not that, why do it?