Most important thing is that villain is a term for a being not for an effect or phenomenon! Illuvitar was not a source of evil or creator of chaos, he was the creator himself, evil was one of the lesser manifestations of his nature as is in a God, it does not represent the god itself! For eg- Matter comes from the The Absolute God but are his inferior manifestations, and he is not affected from them. The true villain is Melk0r himself, the master of Sauron. In broad sense, Sauron can be said as villain in the Lord of Rings but Sauron was doing only what Melkor would have done in his place. The seed of all evil was implanted by Melkor himself when the Music was being sung.