The Morgoth's Ring idea came from a letter or something along those lines so it's hardly set in stone. His dominance over Arda for such a long time before the initial intervention of the Valar and the amount of his own energy put into it is similar to what Sauron did with The Ring but on a worldwide scale. So perhaps early elves prior to travelling to Valinor would be easier tempted and the effect be deeper since this happened literally at the beginning of elves being in the world. It seems the higher up in the pantheon you are the greater but less direct your power is. Saurumon could bend people with his voice, Sauron could bend Numenor to his will through manipulation and Morgoth can influence the very fabric of creation but they all take a degree of permanent power invested in doing so.