The Eagles are not bound by earthlings. That is something that the dialogues between Gandalf and Thorondor sets clear. It is akin to Tom Bombadil's unwillingne

The Eagles are not bound by earthlings. That is something that the dialogues between Gandalf and Thorondor sets clear. It is akin to Tom Bombadil's unwillingness to keep the ring and/or defend Middle Earth: in some sense, it is not their problem (as in NMP). So: they could have done the job but they probably would not have gone to the meetings or accept it because they are above that issue.