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Cody Rhodes left because he knew Punk had Tony wrapped around his finger to the point where Punk was essentially booking Tony's wrestling company, whispering in his ear to change this and that and Tony like an impressionable mark went all along and did everything Punk said.
At that point it stopped being All Elite Wrestling and it became All Punk Wrestling. Cody knew it was over. So he left. Smartest guy in the room, Cody Rhodes.