Without weirdness like Bombadil or Bilbo I fear Lord of the Rings might stray too far into 'sword and sorcery' territory, a world of rights and wrongs and muscular heroes. But it doesn't. It is a world with enigmatic figures who cannot neatly be put down on one 'side' or another. Bombadil brings depth and interest. He, along with figures such as Shelob, Fell Beasts, Dragons, Eagles, Woses and Barrow-wights, shows us that this is a diverse world, populated by beings outside the usual Elf/Man/Dwarf hierarchy.
In our own world we have Men as a species, plus a lot of animals we understand (or at least think we do, who can explain the mind of the domestic cat?
), but we also have creatures we do not understand. We have tales of Loch Ness Monsters, Yetis, Boggarts, Fairies, etc. Had Tolkien created his own world
without all of these types of things then it would have been all the more poverty stricken, grey and depressing for it.
Stylistically, if one of Tolkien's aims was to create something he could dedicate to England then it was only right that he create something with odd, enigmatic figures in it, such as are found in English folklore already. And narratively, those three chapters with TB form a valuable bridge between the familiarity of The Shire to the more perilous realms; the Old Forest is a foreshadowing of Fangorn, the Barrow Downs of the Paths of the Dead or Shelob's Lair.