Good points on power level...
If a character wanted to change professions, I would ask
myself, "have I done everything I could so that this character was needed/interested in the world/game?"
The "worldbuilding" point is a good one. I have actually asked players, "Are you having fun with your character?"
Kind of like "what do you want for your birthday?" This doesn't change the profession, but lets me know where
they think their character/involvement with the world is lacking (for them).
Again, doesn't answer the main topic. I guess it's my way of avoiding it.