Pres. Eisenhower and other from the past didn't salute. This is a recent phenomenon. And, as for the military, the POTUS is only CIC when called into service, and doesn't have have sway of large amounts of our forces like our National Guard, unless they are mobilized by Congress.
Congress has more power and authority than the POTUS.
Saluting became a image concept to grant more a 'authority' like presence to someone, and is great for the sheep who prefer image over substance.
Who is CIC the rest of the time?