I would not like to be CEO of a sporting organisation and find myself in a situation where the biggest and most important corporate decision (strategically as well as operationally, incidentally) is beyond my competence to make.
Choosing and recuiting a Head Coach is a hugely important issue, I would have thought, it should be one that the CEO is fully capable of handling, yes, with input from the experts. But if coaching is a black box to the CEO (beyond his ability to comprehend and manage), he is up against it, IMHO.
Put yourself in the situation of being CEO of an AFL club. Could you recruit a coach? Unless you know a lot about the sport, you would be putting a decision that vitally affects your ability to deliver the goods in other people's hands, totally.
It's okay when things are going well. But when things start to get a bit sour, that's when the rubber hits the road, and an in-depth knowledge of the game and the people who are successful at playing and coaching on and off the field becomes crucial.