Fair point, but one that might seem stronger to someone raised in Celtic lore. For us ignorant Americans the Fomor are pretty darn esoteric -- most modern fantasy that talks about the Fae doesn't talk about the Fomor (Tolkien, Gaiman, Susannah Clarke, etc.).
If I were going to compare Tolkien's Elves to the Fae - which I wouldn't, as they are different in every imaginable way - I would say that the exiled Noldor would be the equivalent to Fomor. They rebelled against the gods, slew their kin (the Kinslayings were unimaginably wicked in Tolkien's universe; Elves simply did not fight each other let alone
kill each other), stole the treasured ships of Teleri to sail across the sea (and then burned them, which was also very evil in context) and wage a doomed war on an evil god while becoming pretty nasty themselves. Indeed, while their war against Morgoth was doomed from the beginning, it fell apart earlier than it might have because of their misdeeds and treachery.
By the time of the Lord of the Rings, Galadriel is the last of the Noldor (edit: Well, there were a couple of others come to think of it, but she was the main one that mattered) in Middle-Earth, and she's ancient indeed - probably only Cirdan, the shipwright you see at the end of the movie, is older, since he was among the first elves that awoke in the world. She was one of the better Noldor, but that scene where she considers taking the Ring shows (by WoT) what her ambition was for thousands of years.
Nevertheless, I feel uncomfortable describing any of the Elves as really evil, like some tales suggest the Fomor are, because they were fundamentally opposed to the one true source of evil, Morgoth. There were no really "bad" Elves - there were some Morgoth was able to enthrall and enslave, but no Elf by his own choice ever served Morgoth or his servant Sauron. Even Feanor and his followers were just really deeply misguided (and later bound, against their will, by their oath - and no, that's not a similarity with Fae, any creature in Middle-Earth would have been bound by an oath like that), but still fundamentally "good" and capable of redemption. And heck, if they hadn't rebelled, the Sindar and Dwarves would have been overrun, mankind would have been lost to Morgoth, and the whole history of Middle-Earth wouldn't have been set in motion.