Maybe I'm misinterpreting it, but I don't see Melkor as being nihilistic. He wants to be Master of All to the point he infuses all of Arda with his essence (making it Arda Marred). Of all the beings in Eä that could be said to be nihilistic are Ungoliant and Shelob, as they had no ethos beyond 'consume and spread darkness'. And I think that's because Ungoliant is the Anti-Bombadil, she is the literal embodiment of Melkor's Discord when during The Music of the Ainur whereas Bombadil IS the Music of the Ainur itself minus the Discord.
(I don't think Ungoliant actually has a fëa, spirit, only a hröa, body.)