Flaws in Lord of the Rings... Yes in the book.

As for the Eagles; they are the minions of Manwe, and are not subject to the will or fate of any save by his will. The eagles represent the presence of Manwe in Middle-earth, and even thought He is Lord of the Valar, He is also subject to Illuvatar, essentially God. That theme permeates a lot of literature, lore, even religion. The Eagles are there to remind you that even with all things being considered, God's (Illuvatar's) will is still present in the world.

As for absolute evil; I am like you in that respect. Personally I don't believe in absolute evil, but then I did not write the story. Apparently Tolkien did believe in absolute evil or it's representation in this story. Not surprised there when one considers that JRR was in fact a Christian and Christians for the most part do believe in absolute evil incarnated in Satan.