What?

[Eönwë]

I couldn't have said it better myself, Legate.

But I also have another thought. After re-thinking about the BoLT, it could be interpreted that Ungoliant was the direct action of Melkor's discord, a primeval spirit of darkness (And probably not Ainu, looking at the text), which would mean, that even if Melkor had left after the end of the creation of Arda, maybe Ungoliant would have drunk the light of the Two trees anyway, and evil would have continued.