I had mentioned that as things stand in LOTR, the Appendices work not so much as appendices but as completing the story. This is clear simply from structure, but one can make the argument from the development of the story.
The main tale as it was eventually published ends abruptly with Sam coming back home after visting the Grey Havens and the line, "'Well, I'm back,' he said." This was not Tolkien's original intent. He wrote an epilogue for the work, two versions of which are discussed in Christopher Tolkien's Sauron Defeated (Houghton Mifflin, [New York: 1992] pp. 114-135), in which we see Sam in his family life, interacting with his children. In the second, which Tolkien still expected to put in quite late, Sam is working on the Red Book and begins having a discussion with his daughter, Elanor, in which a few facts about the rest come out, and he shows her a letter from King Elessar, who is coming north. (In typical Tolkien fashion, Tolkien took time to make a few versions of it, which are not actually used in the epilogue, in order to know how it would look in tengwar.) It ends with his looking at the stars with his wife, Rose, and then going back inside, but as he closes the door he hears the sigh of the Sea.
We don't seem to know the exact reason, but from his correspondence, we know that Tolkien was convinced simply to drop the Epilogue -- apparently everyone thought it should be dropped. But, as Christopher Tolkien says, "He seems both to have accepted and to have regretted that decision" (p. 132); he thought that the book was incomplete without something on Sam and Elanor (who satisfies the longing for Elves that had started Sam off at the very beginning of the work), but could not come up with anything else that would work, beyond "the hints (possibly sufficient) in the appendices" (p. 133). Thus the appendices are all that's left to fulfill a function that Tolkien himself thought necessary to complete the work.