First: Yes, there's a joke, and no, it's not watching other people pretend they get it. They actually get it. You're the one who's lost.
And then the gag evolves AGAIN.
The cowbell player confesses he's only trying to make the most of this rare, rare opportunity to play cowbell in a rock song.
Humor is sanity, not insanity.
Why did the chicken cross the street?
To get to the other side!
Now, let's analyze that. I promise, it won't be funny.
Good observation! Let's talk about that!
Anyway, it's a fun alternate interpretation! The joke is conventionally described as an exercise in unexpected literalism but there is some wordplay there as well.
But you're right! It's in there! Thanks to everyone for pointing it out! It was very late when I wrote that thread and I guess I could've been more thorough.