Its actually because the eagles are not just a straight up ally. Eaglea are the servants of the highest god, and that god doesn't really care about the concerns

Its actually because the eagles are not just a straight up ally. Eaglea are the servants of the highest god, and that god doesn't really care about the concerns of elfes and men. Just like the ents also don't really care unless you fuck with them directly. The eagles showing up at the end is more like an 'Oh we were so awesome and heroic that even the high god sees considers this a worthy cause'. The eagles help Gandalf because of a personal relationship