A fine analysis. I don’t read a lot of fantasy (and even less sci-fi), but I have found that the fantasy stories I like the most have plots and characters that would be compelling even if transplanted into a totally different genre (the universal themes you mentioned). The Lord of the Rings is enriched by the world-building Tolkien did, but he could have written it as a space opera or samurai tale and it would still have worked because of the characters he created, the obstacles he put in front of them, and the motivations he gave them.