From your own selected sources, we have Kissinger telling Nixon that the Air Force isn’t designed for this, but has to relay Nixon’s orders to General Haig.

This is a good point. If you think about it Kissinger was just an intern that passed notes back and forth. As a man with zero influence in any real outcomes he should be remembered for his ability to take dictation with aplomb. It is a mystery to scholars why he is regarded as anything at all