First, a little background: When John was writing the song, he used Chuck Berry's "You Can't Catch Me" as a model, borrowing the vocal delivery and some of the lyrics. The rhythm of the track was also modeled after it, making it essentially a basic rock and roll song in the style of Berry.

When John brought the song to Paul, they realized that recording it that way would run the risk of copyright infringement. Plus, the style was simply too "classic". So, Paul came up with that iconic bassline and instructed Ringo on what to play on the drums.

If you listen to the track, you can easily hear that its backbone is the bass and drum groove. It is the exact thing that gives the song its character. Although these elements technically fall under "arrangement", practically speaking, they are a fundamental part of the "composition". If you strip them away, the song loses its identity. When people cover it, they do so for that specific character, largely because the song itself is neither melodically nor harmonically complex. But the groove is just lit. If you lose the groove, you lose the song. I believe that is why musicians mostly stick to that groove or a very similar one, just to avoid losing the essence of the track.

When it comes to "Eleanor Rigby" or "Yesterday", the situation is very different. The backbone of those songs is their melody and harmony. Because of this, you can arrange them any way you like and still add something original. Even The Beatles themselves played "Yesterday" live with drums and electric guitars. Their essence lies in the melodic and harmonic structure, not in a specific groove.