Now this is my kind of reader:
Further to your post, I wonder if you've ever read any of Tolkien's later philosophical musings about his mythology, in particular the essays and drafts collected in the volume Morgoth's Ring. Tolkien says that Morgoth -- the original Satanic figure responsible for the fall of the elves and (implicitly and off camera) the fall of humans -- imbued the physical world with a large part of his evil essence: "Just as Sauron concentrated his power in the One Ring, Morgoth dispersed his power into the very matter of Arda, thus 'the whole of Middle-Earth was Morgoth's Ring'". This explains why, from the elvish point of view, death is the "gift of men" because it gives them a ticket out of the fallen, Morgoth-tainted world. The problem with this from a orthodox Christian perspective is that death is supposed to be the punishment for the Fall and not part of the solution for the Fall. Tolkien was very much troubled by this deviation from orthodoxy and justified it by saying his mythology was just the elves' imperfect understanding about how things worked. But I find Tolkien's mythology/theology to make more sense and it certainly fits better with the idea that evolution "red in tooth and claw" is part of the residue of the Fall.
I think there's arguably an intimation in Genesis of the idea of death as a gift as well as a punishment - not a solution to the Fall, exactly, but perhaps a mitigation of it. After Adam and Eve have taken the forbidden fruit, God declares that Man is to be banished from Eden "lest he put forth his hand, and take also of the tree of life, and eat, and live for ever," which could be read as a suggestion that the only thing worse than a life corrupted by sin is an eternal life corrupted by sin. C.S. Lewis, Tolkien's fellow Christian fantasist, developed this theme in The Magician's Nephew, by having Jadis, Queen of Charn (and the future White Witch) consume the Narnian equivalent of the fruit of the tree of life, which comes equipped with the warning that anyone who eats of it under the wrong circumstances "will find their heart's desire and find despair." When Aslan is asked, later on, about the fruit's effect, he answers: "She has won her heart's desire; she has unwearying strength and endless days like a goddess. But length of days with an evil heart is only length of misery...."
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