That one with Jon running into the door is a great example of why this works. I looked up the original, and Garfield's line in it was "But don't you think running into the door every day will offset the benefits of the exercise?" Seriously.
Having Garfield say that, or even be in the strip at all, isn't necessary to the joke. His only purpose is to awkwardly overexplain what's already being shown, so taking him out actually makes the humor the strip was trying for stronger.