True, but until 1947, many issues of command were fuzzy. The National Command Authority was created and from that no doubt existed that the chain of command went from the President to the Secretary of Defense. The Chairman of the Joints Chiefs is in that chain as a messenger. The Joint Chiefs are not. From the Chairman, orders go directly to the commanders of operational commands such as the Special Operations Command, Centcom, etc. Except for training, logistics and advice, the joint chiefs are left out, as are most post and base commanders. They are housekeepers, not operational commanders.
I see your point, but let me throw this at you: y Wing King got the very last Order of the Sword awarded by the NCO's of Strategic Air Command. Why? He was the operation commander of the 3701st Provisional Wing in Desert Storm, and while leading a cell on a bomb run in Iraq he took a SAM close aboard and brought his BUFF home with fuel coming out of the wings like a firehose.