PS. Before people get their backs up about the word "allegory" because of Tolkien's perceived dislike of it based on that particular quote, feel free to replace the world "allegory" with "applicability". I believe that Tolkien was simply making a semantic distinction in that quote, and there are many other instances of him admitting to the use of allegory.
In the Extended Edition of The Return of the King, immediately after Gandalf and Pippin storm out of their meeting with Denethor, Gandalf says the following:
The old wisdom borne out of the West was forsaken. Kings made tombs more splendid than the houses of the living, and counted the old names of their descent dearer than the names of their sons. Childless lords sat in aged halls, musing on heraldry or in high, cold towers, asking questions of the stars. And so the people of Gondor fell into ruin. The line of kings failed. The White Tree withered. The rule of Gondor was given over to lesser men.
This scene stands out in the movie for how strongly opinionated - and, frankly, ranty - it is, especially for Gandalf. It seems so on-the-nose and elaborate a monologue that it feels like Tolkien can only have intended that passage as an allegory for something. Do the books expand on this passage any more, and do we know what - if anything - Tolkien intended Gondor to be an allegory for here?