Since this is more a philological question, I'm going with this somewhat different take on the matter from noted philologist J.R.R. Tolkien:
Fairy, as a noun more or less equivalent to elf, is a relatively modern word, hardly used until the Tudor period. The first quotation in the Oxford Dictionary (the only one before A.D. 1450) is significant. It is taken from the poet Gower: as he were a faerie. But this Gower did not say. He wrote as he were of faerie, "as if he were come from faerie".
The source for this is his noted essay "On Fairy Stories", pp 3 (PDF). (I have taken one liberty in transcribing it: the PDF to which I linked appears to have dropped the italics. Tolkien used italics heavily; my memory of first reading "On Fairy Stories" includes that customary italicization; so I have attempted to recreate it as best I can. If I got it wrong, that's on me.)
Anyway, it's bracing to hear a professional imply that the use of the term "fairies" stems mainly from a publisher's error. Tolkien certainly knew his field, and was probably familiar with the occasional accident in transcription carrying large linguistic consequences.
For what it's worth, Tolkien did not hesitate to place Feerie - the land, not the inhabitants - in its proper place in mythology & folklore. From the same essay, on page 4:
Faerie contains many things besides elves and fays, and besides dwarfs, witches, trolls, giants, or dragons: it holds the seas, the sun, the moon, the sky; and the earth, and all things that are in it: tree and bird, water
and stone, wine and bread, and ourselves, mortal men, when we are enchanted.
That rather magnificent bit of wordsmithing outlines the beginning's of Tolkien's theme for the essay. I won't issue spoilers, but this admittedly fairly long piece might be of considerable interest to mythology.SE.