My point wasn’t that fantasy needs elves, but rather that when a fantasy setting does include elves, you likely have a rough expectation of what kind of stereotype they’ll fit. That stereotype is the influence I’m talking about.

The “elves are old, somber, magical, close with nature, tall and thin, magically graceful, pale, have pointy ears, have delicate swooping architecture and designs, etc” stereotype is what you’d likely expect from elves if they get brought up in fantasy… And that stereotype is largely influenced by LOTR. A setting can still be fantasy without elves, but including elves in your story will have the reader automatically setting certain expectations about how those elves will fit into your world. You as the writer can choose to conform to (or rebel against) those expectations, but there’s no denying that the expectation exists, and is heavily influenced by LOTR.