Two nights before the 2013 national championship game, Notre Dame held a massive pep rally on South Beach. More than 20,000 fans showed up, including some of the school’s most prominent alumni. At long last, it seemed, the Fighting Irish were back among college football’s truly elite programs, and their supporters were in no mood to be bashful about it.

“Alabama,” the former quarterback Joe Theismann told the crowd, “I hope you’re listening, ‘cause we’re comin’ for you.”

Nearly...