I don't mind the top brass having all the jointness and schoolness in the world. They are bureaucrats, not operators anymore. An average operational background is probably good enough, but if they don't have a sound foundation of international relations, domestic policy, glad-handing, etc they're going to have a tough time as CSAF.
Now operators on the other hand should be able to choose to stay in their chosen profession and become tactical experts without the up-or-out problems of the current day.