I know what you mean and I wonder about it myself for a while now or much longer. It's like he is more than CiC… It's one of the reasons I post him saluting o7, anyway maybe it's all explainable and you can find it here: https://constitution.congress.gov/browse/essay/artII-S2-C1-1-11/ALDE_00013473/
"Under the Constitution, the President, in addition to being Chief Executive, is Commander in Chief of the Army and Navy. He holds the prime responsibility for the conduct of United States foreign relations. These duties carry very broad powers, including the power to deploy American forces abroad and commit them to military operations when the President deems such action necessary to maintain the security and defense of the United States."