well, as you said, this whole universe was created by Tolkien and he decided everything, in the case of Frodo there is a specific letter from Tolkien that says he didn't become inmortal.
Unfair? maybe but you can say that Tuor carry on an even more important task than Frodo, and he was married to an Elf and was the father of one of the greatest sons of Iluvatar, you could say that Beren should have given inmortality as well but, as it was settle by Iluvatar, the destiny of men wasn't to be inmortal and not everything was said in the music, the valar often would deal with situations that were known and then they would deal with Iluvatar, as the supreme being, Iluvatar didn't need to justify his actions, you could say that his decisions were beyond the understanding of elves, men or even valar, he could decide one way in the case of Tuor and a different way in the case of Frodo.
Of course, Iluvatar could have decided to give Frodo inmortality, but he didn't
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