I think your argument falls down because Frodo is not destroyed in the end, simply wounded to the point where he must leave to be healed. But all mortals have to leave eventually anyway and they do not normally live out their remaining lives in the Blessed Realm.
Frodo could have refused, too.
There is a lot of interesting material on this in Unfinished Tales and Morgoth's Ring. In UT there is a fairly long piece where Gandalf, Frodo, and Gimli discuss the question of who was appointed by whom and the issue of free-will.
Morgoth's Ring also has a long section (Part 4) dealing with the Elves' idea of "estel" which is hope born out of a total trust in Eru's plan even when there is no way of understanding it. It's very interesting.
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