Re: Tom Bombadil
JRRT put much thought over many years into his cosmology of Eru and Arda. After he had categorized the Creator, the Ainur, the Valar and Maiar, the Enemies, the Quendi in all their subcategories, the Naugrim, the Ents, Humans and their subcategories, and all creatures great and small... did Professor Tolkien feel that his world was bereft of mysteries? Linguists, historians, adventurers, and readers of all types have fallen in love with Arda and have tried to systematize it. I confess, that I have.
I worked on making my own Tolkien dictionary until I discovered J.E.A. Tyler's The New Tolkien Companion in 1981. Then I lived vicariously through Tyler's painstaking work.
Perhaps Tom Bombadil is Tolkien's reminder that there are things out there beyond our ability to understand and categorize. Eru's plans and Eru's purposes are too deep too fathom. Inscrutable.
How much fun is it when the supernatural is conveniently systematized?
Have you ever played Dungeon and Dragons? So many players know the rulebooks on the Planes, the Monsters, and the Gods through and through. They cannot be surprised by anything the DM throws at them. And if the DM creates something totally new and homegrown, the players throw a fit and cry foul because this new entity is not covered in the official published systematic cosmology. I ask you, how much fun is that?
C.S. Lewis put it this way in The Last Battle, "Do you think I keep him in my wallet, fools?" said Tirian. "Who am I that I could make Aslan appear at my bidding? He's not a tame lion." The words not a tame lion are repeated throughout the the series, iirc. The point is that if we can figure out every aspect of the supernatural and every characteristic of the divine, then the supernatural and the divine are not really special. In other words, the supernatural is not super and the divine is all too human.
Tolkien and Lewis were human. Yet is seems to me that they were not the tamest of writers.