That's all true, in principle. But the idea of the story was that Kirk wasn't thinking solely about the mission, but was using the mission as an excuse to get his command back. Everyone else kept telling him that it was a mistake for him to kick Decker out of the center seat, and they were proved right when Decker needed to countermand Kirk's misguided phaser order during the wormhole incident. The arc of the story, at least its first half, is largely about Kirk coming to recognize how his obsession blinded him.
That's right but it still doesn't explain why Decker's grade had to be reduced. Even if Kirk has to go back to the rank of captain (for some reason which apparently doesn't apply in TWOK), he would still be the commanding officer and senior to Captain Decker.