Part of my enjoyment of genre franchises is looking for and appreciating continuity. The other side of that coin is, of course, pointing out continuity gaps. But a plot hole is just a plot hole, and means nothing without context. A logical inconsistency in a tense psychological courtroom drama would be more serious than a logical inconsistency in a jukebox musical. I don’t read Larry Niven for his dialogue, and I don’t read Jane Austen for action sequences. Romeo doesn’t check whether Juliet is still breathing, but 1) he’s a character in a tragedy, not a first responder in a police procedural; and 2) Shakespeare was telling a story about young lovers who made rash decisions, so drinking the poison is totally on-brand for Romeo.
Tolkien was telling a story about the power of a humble, arduous commitment to the greater good can undo an otherwise unstoppable force of self-centered evil. I’ve never lost sleep over why Gandalf didn’t ask the eagles to fly the ring to Mordor. Just as Isengard, the Rohirrim, Minos Tirith, the ents, and all the hobbits Frodo left behind in the Shire were perfectly content to mind their own business, it’s consistent within the world Tolkien created for the eagles not to play a leading role. (There are other strategic reasons, such as the fact that Sauron had his Nazgul patrolling the skies, presumably looking for just this kind of incursion.)
The real answer to why the eagles couldn’t just fly the One Ring to Mordor is that flying Frodo and Sam to Mount Doom is a completely different story from their long, lonely struggle against impossible odds. You might as well ask why Elrond and Gandalf didn’t raise an army to invade Mordor, and then throw the Ring into Mount Doom. You might as well ask why they didn’t just take the Ring’s power for their own.
Tolkien invented the eagles for The Hobbit, and used them sparingly as a fast travel system for his wizard in The Lord of the Rings. Boyens, Jackson, and Walsh brought them to the big screen in all their feathered glory. The eagles have an explanation, but they don’t really need it. The plot of the Lord of the Rings is the story Tolkien, Boyens, Jackson, and Walsh wanted to tell. A story with occasional giant eagles. –Susana Polo, Polygon