Disagree.
Tolkien was very clear that he was happy for readers to find deeper meanings in his works. He just objected to writers ponderously enforcing allegory, as Lewis was prone to do.
One is the freedom of the reader, the other is the tyranny of the author.
If anybody is interested, I could talk all week about how Tolkien's world has deep inner meaning applicable to the great challenges of the 20th century.
For starters, his Dark Lords start off as good guys, sincerely trying to bring a little order out of chaos for the good of the people. When the people don't cooperate fully, they're forced to use more and more coercion to maintain progress towards the ultimate goal, again all for the good of the people. In the beginning.
The good guys, OTOH, such as Gandalf, never even attempt to force someone else to follow them, respecting that person't free will as a gift of God.
If that paradigm isn't relevant to the history of the 20th century, I don't know what would be.