[Bêthberry]

One of the points which intrigued Tolkien about literature was stories that are liminal, or on a cusp, of change between epochs. This was one reason why Beowulf interested him so much. His comments on Sir Gawain and the Green Knight suggest as much as well, although it is a shame he never elaborated on his brief comments there.

So, it's just my personal opinion of course, but it strikes me that one of Tolkien's strongest interests in writing LotR was to consider this change of ages, from the Third Age to the Fourth, from the end of the elves' dominion to that of man. Moving right into the Fourth Age, with a clear sense of the passage of the old ways, would give him less scope for exploring such historic changes.

So the poignancy of the end of LotR belongs not only to the simple passing of the characters West but also to the end of an era or age, once that cannot be returned to.