Good cannot be linked with pure in Tolkien's creation as otherwise we would have very few if any heroes. All of them are flawed, even those who are incredibly good. So Good cannot be defined as Flawless.
Now, of course Eru's plan is 'good', but who does this idea of good belong to? It belongs to Eru. It's his 'good'. Which may in fact include a lot of what is 'bad' or 'wrong' or 'tragic' in the eyes of those in his creation.
Eru says that nothing can be done in his despite, which means that even 'bad' things are
allowed by him. Simply put, he creates free will from the very beginning, and that the name Illuvatar means all-father, universe, everything, suggests that Eru is All. Illuvatar is his name within the world he creates, and outside it, wherever he is, in the void maybe, he is Eru, which means The One, which suggests that he is everything, and if evil exists then he must also be that too.
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There was Eru, the One, who in Arda is called Ilúvatar.
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When the Ainur sing the Music they are creating a 'map' of everything that will exist in the world Tolkien creates; Melkor creates discordancies, and again:
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no theme may be played that hath not its uttermost source in me
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Considering that Melkor and Melkor's works, and Aule's meddlings with creating Dwarves and the Valar's creation of Numenor all ultimately stemmed from Eru works. It makes sense of the fact that evil has been built into the fabric of this world from the very beginning (different to Middle-Eastern originating views of our own world where there was a Fall - there was no Falling to be done in Arda as there was no state of grace to begin with due to Melkor's discordancies...if there was a state of grace it was presumably when there was nothing
but Eru, seeing as he says he created
everything).