There is no reason the Air Force should be or should have been extended to patrols of outer space. It would be natural for the Navy to undertake these tasks.
I disagree I think the Air Force can handle the job better. Navy to me is more of sea based service..
All the speculation of a hundred years of science fiction indicates that the culture and tradition of the Navy will be that of the space force.
All space terminology in science fiction, including personnel rank names comes from naval origins.
Examples: hull, bulkhead, midshipman, commander, admiral, "all ahead full"