But there's trouble with that theory as well, because it's the "just the way it is," theory.
For example, why is D&D so popular, that it is the granddaddy of RPGs? Is it because of Tolkien? (Thus discounting Empire of the Petal Throne)? Well, then you'd have to account for Tunnels & Trolls, which was published around the same time and had (wait for it) Elves, Hobbits, and Dwarves.
That's why it's complicated. The first RPGs that we know of weren't fantasy RPGs (Braunstein, first Arneson). But the one that really took off was a fantasy RPG. Why? Because it was cool. Because it was the early 70s. Is that because Tolkien created the market, of because the market was ready for something Tolkien-esque?
Once you move past the obvious influences (those things brought in from Chainmail, which was itself based on what Perren definitely read, and what Gygax probably read, about a wargame in New England), and those things that are player demands (such as the Ranger), how much is left?
But then, how many players came into D&D from Tolkien?
These are things that are not easily resolvable. Less so because so much attribution goes to EGG, who, despite being amazing in so many ways, also had a bad habit of attributing things to himself that we know aren't accurate. He borrowed from everywhere- myths, pulp fiction, wargaming roots, history, and, um, other gamers ... and it becomes problematic to attribute too much to Tolkien.
In the end, it's an unanswerable question.