Although I watched Letterman for decades, I’m ashamed to admit that I never, ever picked up on the running gag about drums. Whenever a band finished performing and Dave walked over to talk to them, he’d almost always ask about the drummer’s kit.
Why? Probably not because he had that much of an interest in drums. My guess is that he was just trying to loop the guy at the back into the band into the spotlight for a brief second.