So I guess an executive, decision-making position in a business (i.e. The Real World) doesn't rate? All I'm seeing is how many paychecks these candidates have collected from taxpayers.
Some helps, but "too much" is probably not good either. Different arena. Remember Robert Strange McNamara, who went from head of Ford to SecDef. What a FReaking disaster he was, and still is.
Ike's "military" experience had large measures of management and diplomacy as well, and really very little classic "military" type experience. That included his time in the Philippines as well as his later role as Supreme Allied Commander in Europe.