I will begrudgingly agree that Tom isn't needed to tell the story of the fellowship.
However, it's a much smaller and blander world without Tom. The fact that he's never really explained in the trilogy, and that he shows up relatively early, really drives the point to the reader that this world is OLD, and that the story we're currently following is just one of the many, many stories that this world has seen and will see in the future.
It puts things into perspective: yes, the task of the fellowship is critical, and it's outcome will probably dictate what the New Age will be like. But it's just one story - the world saw many before them, arguably even grander, and will probably see more stories and new ages, even if they fail.
This is what really made me fall in love with the Lord of the Rings. It escapes that Hollywood feeling that the now is the only thing that matters, and that it has to be the biggest baddest most spectacular thing ever.
It really doesn't, and that doesn't take a thing from the story being told. Tom's aloofness puts this into perspective for me, and his absence makes the universe of the movie much more linear and boring.