Not the OP, but I think in FotR the Bombadil interlude is an unnecessary distraction that saps a lot of the momentum from the story, and it’s tonally inconsistent with the rest of Middle-Earth (as seen up to that point). And the character simply has little relevance for the entirely of the book - only briefly mentioned at Elrond’s council and then in Return of the King, and never actually revisited. His only tangible impact on the plot involves giving the blades of Westernesse, which could have been accomplished in a much more straightforward way. In general the Bombadil scenes are confusing, even to dedicated Tolkien fans, and only detract from the book.

For the film, it is really the pacing issue that is most crucial: FotR is already a long and complicated movie, and it really doesn’t have a second to spare on unnecessary scenes. And, unlike a book, movies can’t really be digested slowly (especially not in a theater). The Bombadil scene is a small oddity in the book but it could have been a fatal flaw in the film, disengaging audiences before we even get to Bree.

I think Bombadil could have been effective later in the trilogy - where the fact that the Ring has no affect on him would carry more dramatic weight, and where the “tonal inconsistency” would be surprising and refreshing rather than confusing. Perhaps shortly after meeting the Ents - it would strengthen the idea that Bombadil is vastly powerful (even compared to Sauron) but aloof from human/elf/dwarf concerns.

For much the same reasons as ojnabieoot gives above. The Bombadil chapters feel like a haphazard insertion from a different book and perhaps even from a different fictional universe, and seem to serve no narrative purpose in the context of the trilogy. The film version feels much more coherent for having omitted them.