Eh what fun would that have been?
I think the eagles were maiar, i dont think they were allowed to help without permission when it came to matters involving the other maiar ie: Sauron, Gandalf. I suppose the reason they were able to rescue Gandalf from Orthanc, would be that Saruman(also Maiar) broke the rules.
Thank you, someone who reads Tolkien's work, including his letters
This very thing was addressed right after Fellowship of the Ring was released, many fans wondered why they didn't just fly on the backs of giant eagles..These are in his "letters" that his son releato the public after his death..
The eagles were maiar spirits, not of the same rank and power as gandalf and saruman, who were once mighty "angels" so to speak. After the end of the second age, when Numenor was drowned because of Man's supreme arrogance, The valar, who are the creators of the universe under the guidance of Eru, the One, decreed that the great spirits were not allowed to interfere with Middle-Earth and the remnants of Beleriand. Of course, there were bad maiar spirits like sauron who said fuck you and did what they want.
Since that includes races such as Eagles, and Beorn-Men (were-bears) could not fight for the fate of middle-earth, even though they lived there.