Of course it's exceptionally probable that these rear area units would have suffered greatly from nukes.
It's most probable not very many naval or aviation personnel survived.
Those few Air Force personnel remaining, particularly ground crews and pilots, would be far too valuable to reassign to army units. There might not be any fuel to actually fly the handful of planes left more than once every few months, but they'd still require maintaining "just in case".
Naval personnel are in my mind more likely to be reassigned to the army (and a few going to support what's left of the Air Force).
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If it moves, shoot it, if not push it, if it still doesn't move, use explosives.
Nothing happens in isolation - it's called "the butterfly effect"
Mors ante pudorem
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