I personally think some of the fairy tales of George MacDonald and CS Lewis are better.
I'm glad Tolkien did not take the advice of Auden, the book would have not been as good without the story of Arwen.
Beren and Lúthien Tinúviel set the stage for what had to be. Aragon needed his Arwen. The myth parallels biblical similarities and so you are right; the trilogy would have failed to illustrate this important relationship between men and elves.