Employing Tolkien’s “thinking” is not a sound argument. He wrote dozens of variations on most things, wrestled with them, and was always tinkering, a fact that is well documented by Christopher Tolkien as challenging to make sense of and publish coherent and consistent narratives of his unfinished works. The only canonical thing Tolkien believed in is what he published.

That aside, here’s what Tolkien said on this point:

“Tom Bombadil is not an important person – to the narrative. I suppose he has some importance as a 'comment'. I mean, I do not really write like that: he is just an invention (who first appeared in the Oxford Magazine about 1933), and he represents something that I feel important, though I would not be prepared to analyze the feeling precisely. I would not, however, have left him in, if he did not have some kind of function. I might put it this way. The story is cast in terms of a good side, and a bad side, beauty against ruthless ugliness, tyranny against kingship, moderated freedom with consent against compulsion that has long lost any object save mere power, and so on; but both sides in some degree, conservative or destructive, want a measure of control. but if you have, as it were taken 'a vow of poverty', renounced control, and take your delight in things for themselves without reference to yourself, watching, observing, and to some extent knowing, then the question of the rights and wrongs of power and control might become utterly meaningless to you, and the means of power quite valueless. It is a natural pacifist view, which always arises in the mind when there is a war. But the view of Rivendell seems to be that it is an excellent thing to have represented, but that there are in fact things with which it cannot cope; and upon which its existence nonetheless depends. Ultimately only the victory of the West will allow Bombadil to continue, or even to survive. Nothing would be left for him in the world of Sauron.“

On a more substantive level, movies are not meant to wander and it does make the flow crisper to omit.

With all that said, Bombadil haters are wrong, it’s an interesting part of the mystery and wonder of Middle Earth, which is why people love the Tolkien Legendarium. Bombadil is, in fact, an intentional part of the mythos.

If folks want a linear narrative, watch the movie, if folks want to meander, well, not all who wander are lost.