Well at least Charlie Brown has been studying classical composers in preparation for his little talks with Schroeder.
What we are seeing here is the mining of a situation, slowly, of all its obvious jokes. This is what cartoonists, and indeed sitcom writers, primarily do, they pick a situation and think of ways it is funny, or can be made funny. But the soul of humor is novelty, and a situation can only provide so many jokes.
What happens when all the obvious jokes have been made? In the case of Garfield the strip just continued to mine, reformulating the old jokes as best they could, the characters never evolving beyond their simple personalities. This is actually what happens to most comic strips, and it's why most of them become much less interesting 20 years after their creation. 20 years is 7,305 strips, 7,305 separate, supposedly individual, jokes. By way of contrast, stand-up comedians never come up with all new material for every performance.
Cartooning is a difficult-enough business to get into that most young hopefuls focus on the short term, impressing the syndicate gatekeepers enough to get into the business, and not with how they're going to maintain their work for decades. The great Bill Watterson, perhaps recognizing how hard it is to keep it up until your keel over at the drawing table, wisely stopped Calvin and Hobbes just over ten years in. But ten years in Peanuts was in its prime.
This is worth mentioning now because jokes about knowledge of classical composers are already approaching the limits of how far they can go. What Schulz is doing, slowly, is segueing from jokes about situations (composer knowledge) to jokes about character types (musicians), and eventually to jokes about specific characters (Schroeder).
