There are few current politicians, if any, who qualify as intellectuals or academics. Harold Wilson was the last Prime Minister to fit the description (he had taught economics at university). Gordon Brown was able academically as a young man, but was no economist when he became Chancellor of the Exchequer.
The job of Minister requires political skills and experience, plus common sense and an ability to organise and persuade..It's not a job for academics or for intellectual skills and ability.Intellectuals and academics are to advise the Minister. In this case, there'll be experts on military matters and defence to do that.We should worry more if the advisers don't have intellect or expertise in their field..
Plus, of course, a minister is normally selected from the MPs. Being chosen as an MP requires no particular intelligence or brains whatsoever (as, you may feel, is regularly demonstrated).