That's a military command with lots of military units that reports to Strategic Command. NSA sort of administers it even though it's not really theirs. Even if we count them as NSA, that would fall under SIGINT in my division of their activities. It would still be SIGINT rather than IAD doing that stuff. So, splitting off IAD wouldn't affect the analysis whether it's NSA's teams doing SIGINT or NSA + STRATCOM's sub-commands doing it with NSA SIGINT personnel.
The premise of this sub thread is that cybercom and NSA proper have fundamentally different missions, in part because they are governed by fundamentally different legal frameworks, and it should therefore also be split from NSA proper. It was not an argument that IAD should not also be split off.