Well, obviously. I mean, the goodies have access to giant eagles and all they have to do is to give the ring to one of them and drop it in Mount Doom and the whole thing is solved, right?
Wait, it must be that eagles are easily corrupted? Or not fully sentient, and thus the ring can control them?
Maybe they would, maybe they wouldn't. Big risk either way.
Anyway, this theme is why the most meek people of Middle Earth -- the Hobbits, who desire basically nothing more than a quiet life -- are the only ones in Middle Earth that could actually cart the ring into Mordor. Even then it's not a sure bet, considering Gollum.
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