Down Goes Brown ranks every Gary Bettman Stanley Cup presentation. This is a prima facie case for Betteman stepping down, or at least giving up the ceremony (scroll down a bit). From the ‘Canes 2006 win:
The Handoff: 11/10. A total disaster. First, Brind’Amour shows up early, leading Bettman to scold him by yelling “I’m almost done” into a live microphone. Then, when Bettman finally finishes rambling on, Brind’Amour takes the Cup rather than waiting for the commissioner to give it to him. He just rips it out of Bettman’s hands and immediately starts making out with it. This is one of the greatest hockey moments of all time.