Fourteen years ago during the eighth season of Fox’s “American Idol,” Simon Cowell was one of the people who judged aspiring singer Adam Lambert on a weekly basis. Even though Simon critiqued Adam early on for being too theatrical, Simon soon became one of his biggest supporters. “Over the entire season, you’ve been one of the best, most original contestants we’ve ever had on the show,” the British judge declared during that show’s 2009 finale. “The hope and whole idea of a show like this is to find a worldwide star, and I truly believe we’ve found that in you.”

Flash-forward to 2023, and the two popular personalities reunited during the season finale of NBC’s “America’s Got Talent: All-Stars.” Simon was seated at the judges’ desk (next to Heidi Klum and Howie Mandel), while Adam was up on the big stage performing his version of “Chandelier...