Schroeder actually doesn't do much in the past three strips other than play the piano. The humor comes mostly from the other characters reacting to it. A tremendously silly thing is not as funny as people dealing with it.
As the strip gets older, the characters eventually kind of become creatures of their settings. Schroeder eventually becomes seen in few places other than before his piano, which also means that Lucy, the other resident of their little two-kid pocket universe, becomes his main contact with the rest of the Peanuts world.
