Remember back when people the internet were asking why the fellowship in the Lord of the Rings didn't just ride the eagles to Mordor? Well, many people have called it a plot hole, but then many other people rebutted by pointing out all sorts of reasons that wouldn't work.
My favorite rebuttal is that since the giant eagles are sapient beings that are possibly Maiar spirits in bird-forms the way Gandalf and Saruman are Maiar incased in humanoid forms, chances are they are just as easily prone to temptation as the wizards were shown to be (btw, Sauron and the Balrog were also Maiar, albeit ones that had been led astray into evil during the dawn of time).
Image Links: https://artmctalon.artstation.com/projects/m8xV4d https://artmctalon.tumblr.com/post/756760689543086080/raptor-and-the-one-ring
Music: "Sci Fi" by Bensound (https://www.bensound.com/)