The first time I can recall hearing Casey Kasem count down the hits on American Top 40 was on a Sunday in June 1981. Just shy of 10 and in the car with my cousins driving to the beach, I asked them to stop flipping the radio when they landed on Kasem, who was just a couple of songs away from revealing that week’s No. 1 hit. I’d glimpsed Kasem once or twice before that, on America’s Top 10, the television version of his countdown show, which ran on Saturdays after cartoons ended. But hearing Casey on the radio that...