[NOTE: This post is not claiming that all callings are inspired - or even that all leadership callings are inspired. I don't believe that. However, I believe many are - and this post address those that are.]
I believe that there is something everyone can learn from every calling they fulfill, but I don't think the Lord wants an entire ward or stake to suffer in order for one person to grow. In my experience, however, when it comes to truly inspired callings of Bishops and Stake Presidents (and auxiliary and priesthood presidents), there generally is a particular reason that a particular person is going to be needed in the future - so that person is called.
I have experienced a ward that went through certain problems that required a very strong, single-minded, no-nonsense, "iron rod" Bishop. A soft-spoken consensus builder would have been eaten alive and spit out. (I mean that seriously. The ward might have imploded.) The Lord knew in advance what trials that ward would face, so he called someone who could handle those trials - even though some other issues arose as a result of some members not reacting as well to such a personality. When those trials passed, the Bishop was released - and a soft-spoken, incredibly humble and gentle man was called to take his place. It was revelation through the Stake President in the truest sense.
Each was the right person for his specific time because of the particular strengths each possessed that were a perfect match for the issues of his own administration. Yes, they learned lessons while they served, but I am convinced that their learning of those lessons was not the primary reason they were called. They were secondary to the needs of the body of Christ they led.