I think I agree with you, overall.

But I would say that Bombadil is hugely important to understanding Middle-earth as a crafted mythos. He gives us valuable insight into Tolkien's ideas about self-satisfaction (the Ring has no sway over Tom because he is his own master), relationships with the land (Bombadil is married to a river spirit), being gentlehearted but stern (accepts the Hobbits gracefully, but defends them from Old Man Willow ardently), and a host of other things. He's like a distillation of what The Lord of the Rings is "about", in a sense, without having much direct impact on the story proper. He also serves to give depth to the world: we are introduced to him as just this sort of enigmatic fellow who deus-ex-machinas our protagonists out of a tight spot and then we move on, but then half a book later we find out the the most learned of the Elves hold Tom in such incredibly high esteem they consider whether to send the Ring to him (and, if I recall, doesn't Treebeard make mention of Bombadil at some point, too? further suggesting his importance to the world at large).

But he is not important to the plot, nor does he really serve to move our characters along their respective arcs in any meaningful way. His chapters really establish, with respect to these elements of the narrative, just a few important things:

- He demonstrates that the Ring's power can be resisted, but it does not come easily.

- He arms our Hobbits, which of course comes in handy at the Battle of the Pelennor Fields.

- The calm of his house nestled in the chaos of the world gives rise to Frodo's foresight of his travel to Valinor: "the grey rain-curtain [...] rolled back, and a far green country opened before him under a swift sunrise."