On questions such as yours, I always refer back to Reagan's bombing of Tripoli.
The mission was presented to the Joint Chiefs and it was pretty much agreed that it could most easily and effectively be handled by Navy and Marine Corps air being flown from the decks of Navy aircraft carriers. The Air Force squealed like pigs that they were being shut out and that such a move would dramatically hurt them when it was time for budgets.
Things got ugly and very complicated. Only the English would allow U.S.A.F fighter/bombers to carry out such a mission from their territory. Then, it became a matter of gaining permission to use airspace over all countries between England and Libya and then there was the bit about in flight refueling and concerns about pilot fatigue.
Very few of their pilots air qualified to conduct carrier based landings so that put a definite cramp on contingency plans.
Then there is the argument about the Army VS Marines. The Army is much bigger but has not been "First In" since Korea. They're no longer designed nor train to fill that roll. They are however a great occupation force, which frees up the Marine Corps to conduct the aggressive operations. On that, they are a great compliment to one another.
Which means, to answer your question, it is the Air Force who is least necessary. They do by the way, now train to conduct carrier based operations.