This has always been my understanding of Bombadil as well. The most popular/accepted view of who he is among Tolkien-dom that I've heard is that he represents the lands of the West themselves (or perhaps all of Middle-Earth?). In the Tolkien legendarium power comes from knowing the right names for things and the right words to say to them. Tom Bombadil is the most powerful being in Middle-Earth because he is so old that he knows the proper name for everything and how to address them (he chastises Old Man Willow to release the Hobbits like he is a child).

I do want to credit the author of this post with the observation that the rulers of lands in Tolkien's legendarium have influence over how those lands express themselves, but I think this letter is the answer to that. Tom is the exception; he eschews power. One of Gandalf's reasons for saying that they wouldn't want to give the ring to Tom is that he would probably lose the ring, not thinking it very important. Tom only cares of eating and drinking and making merry. In that regard he is a Dionysian figure. If you read the Adventures of Tom Bombadil (which this author surprisingly doesn't reference) he is clearly modeled on the Dionysus cycle of myths.