One of these things is not like the others...

[Raynor]

Which is why we are fixated upon and fascinated by the likes of Bombadil, the Stone Giants, the speaking thrush, Beorn, even Orcs/Goblins, Trolls and Dragons, Werewolves, Vampires and Wargs.

Some of them are, indeed, intended enigmas - such as Bombadil:

Originally Posted by Letter #144

And even in a mythical Age there must be some enigmas, as there always are. Tom Bombadil is one (intentionally).

Though I can't recall the letter at the moment, he did state that he wanted others to continue his cycle. The stone giants are a passing refference - but we do see pairs of good evil for almost everything - even Tulkas represents the good side of violence cf Myths Transformed, so maybe Melkor's (?) evil trolls have good counterparts - as in the Letters and in LotR, he rejects the idea of something completely evil. Concerning speaking animals, Tolkien did complain about it:

Originally Posted by Orcs, Myths Transformed, HoME X

What of talking beasts and birds with reasoning and speech? These have been rather lightly adopted from less 'serious' mythologies, but play a part which cannot now be excised. They are certainly 'exceptions' and not much used, but sufficiently to show they are a recognized feature of the world. All other creatures accept them as natural if not common.

The rest of the bunch are indeed interesting, Beorn, wargs, werewolves, etc, but I do think that their primary home, of all the possible humanly conceivable ones, is in fantasy. That is their right place, and they fit with the laws of the created universe, and therefore have a positive participation to the success of the story, not the other way around. However, I do believe that there were things that were beyond what he deem possible to correct:

Originally Posted by Letter #131

It is not possible even at great length to 'pot' The Lord of the Rings in a paragraph or two. .... It was begun in 1936 and every part has been written many times. Hardly a word in its 600,000 or more has been unconsidered. And the placing, size, style, and contribution to the whole of all the features, incidents, and chapters has been laboriously pondered. I do not say this in recommendation. It is, I feel, only too likely that I am deluded, lost in a web of vain imaginings of not much value to others — in spite of the fact that a few readers have found it good, on the whole. What I intend to say is this: I cannot substantially alter the thing. I have finished it, it is 'off my mind': the labour has been colossal; and it must stand or fall, practically as it is.