LotR was my 1st intro to Tolkien - I read The Hobbit afterwards, about 18 months later. Having read both books many times since (I've lost count but it's at least a dozen times in both cases and far more for LotR), together with the Silmarillion and gradually working my way belatedly through Lost/Unfinished Tales that form a part of the 12 volumes of The History of Middle Earth by Christopher Tolkien - so far I've read Vols 1, 10 & 12
) Bombadil's part in LotR is at once superfluous and contextual in that he and Goldberry are in there to represent 'old Middle Earth' and tie the later story into the beginnings of the legendarium.
Having said that, at 10 years old I skipped through the Old Forest and 'House' after my 1st reading for the following several rereadings because it's of little or no importance to the action
storyline at all. For Tolkien scholars however, Tom Bombadil is Russia. In other words he
Winston Churchill wrote:is a riddle, wrapped in a mystery, inside an enigma
as that whole section is to show very, very subtly the larger preternatural and rather sinister world surrounding the Shire and to underline the sentience of the Ring in that it starts giving Frodo visions at that point (after the magic mushrooms) of Gandalf imprisoned in Isengard and in Bombadil's cavalier handling of it that there are creatures abroad in addition to the Elves and the Black Riders who have a very different relationship with the Ring and, in passing of the existence of Ents as the Old Forest is a relict outlier of the ancient forests that once included Fangorn and spread farther west of the Grey Havens to where the drowned lands of Middle Earth lay before the Ring was even forged.
When you read LotR having knowledge of all that background then Bombadil's chapters assume a depth and breadth that is mind-boggling with complexity and woven myth and you realise exactly why Tolkien fandoms have more than their fair share of lore nazis and why people like one Terry Pratchett have been able to mine Tolkien's creation so consistently for motifs and 'takes' on faux mythology for all kinds of twists and turns in re-spinning fantasy. So yeah - it's camp and it's silly but it's also kind of spooky don't you think that some weird guy dressed in day-glo can actually spring 2 hobbits swallowed by a tree or drive off a barrow-wight about to steal some souls just by singing a load of old toot?
The Adventures of Tom Bombadil
and Tales of the Perilous Realm
also have Tom Bombadil in them - I haven't read them as I'm sure he's still just as annoying but he's more than just a distraction in there and Goldberry is one of the Ainur - the angel-like creatures placed on the Earth to care for it and it's inhabitants. Regrettably, Ainur like Sauron and his own master Morgoth (formerly known as Melkor) weren't quite so eccentric in their duties and their rebellion causes it all to go badly wrong. Bombadil in essence and in tandem with Goldberry is therefore a guardian figure who 'preserves' places like the Old Forest in a semblance of what they should have been and through their combined magic are one of the main protectors of the Shire through their aegis over the Withywindle and then the Brandywine. This in part explains why Hobbitland is so relatively untouched by all the nastiness that other places all around experience as Sauron's power grows in his search to regain his lost Ring.
So - I see where you're coming from for sure Will, but for me Bombadil's kind of grown of on me, not least because of the appallingly bad taste songs