I don't think you can lay the blame on Ilúvatar.
Quote:
[Ilúvatar] declared to them a mighty theme, unfolding to them things greater and more wonderful than he had yet revealed; and the glory of its splendour of its end amazed the Ainur, so that they bowed before Ilúvatar and were silent.
Then Ilúvatar said to them: "Of the theme that I have declared to you, I will now that ye make in harmony together a Great Music. And since I have kindled you with the Flame Imperishable, ye shall show forth your powers in adorning this theme, each with his own thoughts and devices, if he will. But I will sit and hearken, and be glad that through you great beauty has been wakened into song."
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The one option that doesn't seem to have been pointed out is that it could have been
predetermined that Arda would be created. If this were so then the Music would have been the blueprints so to speak for Arda. Ilúvatar intended that this Music, the "blueprints" would be good. When the music started, and Ilúvatar declared his theme, it was good. All of the Ainur, even Melkor, were at this point good. Therefore, Ilúvatar completely intended for the music to be good. The music, was the beginning of the Creation. At this point, while it is unfolding prior to the dischord of Melkor, is when you have Arda Unmarred.
Then we come back to Frodo. I do not believe Frodo's suffering was Eru's will. It was because of the Dischord of Melkor, sin, that he had to suffer. It was Eru's mercy, his Divine Intervention, that he allowed the Ring to be destroyed - because of Frodo's willingness to sacrifice, and because of his mercy and pity to Gollum. Because of this, Eru allowed Frodo to have peace from the Ring, and grant that there may be healing beyond the confines of the world - whether in Valinor or even after. Tolkien doesn't specify what happens to Hobbits/Men after death, but maybe for Frodo there is healing. This would be Eru's mercy to him. It is wrong that Frodo had to suffer, but I do not think that Eru was to blame for this.
Our world is marred by our fall. Would it then be fair to say that Arda was marred by Melkor's fall? Arda unmarred was an option, and it could have been but for Melkor's dischord. We fell. We sinned. But when Christ came, he did not take sin from this world. Rather, he gave us salvation after death. Salvation and healing of all of our sins and hurts in this world. Perhaps this is how it works with Eru as well. Sin in Arda, but something better, perfect, afterwards. Frodo, I believe, found healing somewhere. When/how/where is not specified.