The literary purpose of enigmas is to intrigue the reader, to make them wonder. You don't necessarily have to theorize, but if you're intrigued, and like the mystery, that's what's important.
If you just left Bombadil as a mystery, and didn't approach him with intrigue, then you are missing the point. If you leave Bombadil as a mystery AND are intrigued, that was what I believe was intended with the absence of explanation.
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