Some of the most well-known Lord of the Rings “plot holes” are actually very easily explained.
“Why didn’t they just fly the eagles to Mordor?”
Sauron has air units. Given the lack of any specific numbers given for the number of eagles, the number of those hell-hawk wyvern things the ringwraiths ride around on, and how far off Sauron’s lidless eye would’ve been able to see the eagles coming, we have to assume that all those numbers work out in favor of the conclusion that informed characters in the story come to: Sneaking the Ring in on foot is more likely to succeed than trying to punch through Sauron’s air defenses with the eagles.
“Why wasn’t Mount Doom guarded?”
It’s impossible to willingly destroy the Ring. Hobbits are significantly better ringbearers than Sauron ever accounted for and Frodo still couldn’t manage it. Gollum destroyed it by accident. The fumes from Mount Doom also make it difficult to climb and, presumably, preclude the stationing of orcs on its slopes or especially at the Crack of Doom itself. Frodo and Sam pass out several times on the way up. Sauron totally does surround Mount Doom on all sides with tens of thousands of orcs, and when he moves them away, it’s because he thinks Aragorn has the Ring and is using it to try and attack him at the Black Gate. So when he moves his orcs away from Mount Doom, it’s because he thinks he’s repositioning them so that they’re all between the Ring and Mount Doom, where normally half of them would be on the other side of Mount Doom from the Black Gate.
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The Council of Elrond would have been keenly aware of the Eagles’ participation in the Battle of Five Armies seeing as several of the Council members participated in the battle. They also knew that Sauron had rallied the goblins and wargs of those armies to his banner in the intervening years. So certainly Sauron had equally good information about the Eagles’ potential to engage in the war. The Council had to assume that the Eagles were being watched by his spies as one of the greatest potential pieces in the war. Rivendell alone was a secret sanctuary away from espionage.
Even if you could secretly get a message to the Eagles to cross the Mountains, get the Ring, and take it to Mordor, you still have the fact that Sauron has air defense and the very air of Mordor itself would betray them. Surreptitiously setting out with a tiny band traveling through uninhabited wilderness to sneak into Mordor is still a better plan than an aerial approach.
But even setting all that aside, your second point applies to the first, too. The Eagles are proud, mighty creatures who are susceptible to the Ring’s corruption, as well. Just as Isildur, a heroic and Faithful Numenórean, did not wish to destroy it very quickly once he possessed it, so too would the Eagles. And they may, like Gandalf and Elrond and Galadriel, know the danger it poses and refuse.
You can criticize the book, at least, in that a lot of options were discussed and rejected at the Council (one of which was, ahem, much sillier than the Eagles) and it’s kind of weird this one wasn’t. But an omission of a discussion is not the same as an actual hole in the story logic.
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