I think the incongruity of Bombadil, how he almost seems to break out of the book meta-fictionally — the reason some people have seen his character as an allegory of the reader — could be thought of as showing a certain type of "spiritual awakening."
Consider samsara and nirvana in Hinduism and Buddhism. The epic world of Middle-earth is extremely samsaric. Actually, samsara is the way we all invent our own epic world in life — real life itself is made fictional. Buddhist scholar & monk Thanissaro Bhikkhu writes:
Instead of a place, [samsara is] a process: the tendency to keep creating worlds and then moving into them. As one world falls apart, you create another one and go there. At the same time, you bump into other people who are creating their own worlds, too.
The play and creativity in the process can sometimes be enjoyable. In fact, it would be perfectly innocuous if it didn't entail so much suffering. The worlds we create keep caving in and killing us.
With the words of Hinduism, we have that the phenomenal world is a kind of illusion (called maya), which is a manifestation of a creative divine play or dance called lila. This is literally and obviously true in the case of Middle-earth, of course; it is nothing but the maya of Tolkien's lila. Conscious beings can through different types of yoga (including meditation) see through this veil and achieve total liberation. I would like to suggest that this is what Tom Bombadil has achieved.
In all such religious visions, liberation from "Middle-earth" involves releasing the attachment to the individual self. One's basic perspective shifts to something more universal — like Bill Hicks put it, "we are the universe experiencing itself subjectively." This is called by various names: the deathless realm, the absolute, non-duality, Buddha, etc. In the Zen tradition, koans like "what is mu?," "what was your original face before your parents were born?," "what is the sound of one hand?" all point to this kind of awakening.
All this seems congruent with Bombadil's character. For example, "when Tom Bombadil speaks, it is as if Nature itself — nonrational, interested only in life and in growing things — were speaking." Non-rationality, going beyond words and concepts, is emphasized very much in Zen as the essence of awakening. Bombadil speaks for all living creatures; that's the way of the bodhisattva.
Bombadil says he "was here before the river and the trees ... the first raindrop and the first acorn." This doesn't necessarily mean that Tom Bombadil the individual has been alive for such a long time; when living from the enlightened perspective, one is beyond birth and death. Pure consciousness is just Buddha consciousness.
One interesting hint that Tom is a Vala may be tucked away in the confusing claim that Tom is "the oldest" even though Treebeard is at the same time supposed to be "the oldest living thing that still walks beneath the Sun." In The Road to Middle-earth, published in 1982, T. A. Shippey, who considers Tom "a one-member category," struggles with this "inconsistency" and concludes that the claim that Treebeard is the oldest living thing, if true, implies that Tom is not alive, just as the Nazgul are not dead (p. 82).
As an awakened being, Bombadil is beyond living. In Zen, complete enlightenment is called the great death.
Goldberry answers the question "Who is Tom Bombadil?" with the simple statement "He is."
There are many Buddhist stories like this. A layman comes to the monastery curious about the visiting master. He inquires for him, and is told that the master is out sweeping the garden path. Sure enough, he finds him there, goes up and makes a bow, and asks "who are you?" The master hears the question, but merely continues to sweep. Annoyed and puzzled, he goes back and asks the abbot: if your master is so enlightened, why did he ignore my question? The abbot replies: instead of telling you, he showed you — a perfect answer!
Tom's inability to separate song from his other activities, speaking, walking, working, suggests that it is very fundamental to his being in a profound way that distinguishes him from all other beings encountered in the trilogy.
In Zen Master Hakuin's Chant in Praise of Zazen, an eighteenth century song about the wonders of meditation and realizing one's true nature, it is said that "when our thought now is no-thought, our singing and dancing are the voice of the Dharma."
In general, the hobbit-like demeanor of Bombadil is just like that of an awakened Zen master. A beautiful expression of this can be found in the verses accompanying the Ten Ox-Herding Pictures, which is like a old Zen cartoon strip depicting the journey towards complete enlightenment. In the very final frame, after the great death of complete satori, the fully transformed Buddha enters the regular world again:
Shoeless and bare-chested, he enters the marketplace.
He is daubed with earth and ashes, and a smile fills his face.
Making no use of the secrets of gods and wizards,
He causes withered trees to bloom.
So, as Tom Bombadil is
located at the core of morality as it existed in Middle-earth, as the ultimate exemplification of the proper moral stance toward power, pride, and possession,
I very much agree that such a character is utterly essential to the narrative, precisely because it stands out as humorously incongruous. He symbolizes the true happiness, the possibility of liberation in the very forests of Middle-earth. Tom Bombadil is the embodied principle of awakening from the fictional world of suffering — in which we all live.