>>723131043 (OP)
Basically the only reason Sam and Frodo got as far as they did into Mordor was because Sauron never guessed that the plan was to destroy the ring. He thinks they're doing Boromir's plan.
He thought Aragorn had it, assuming he took it off of Pippin, mistaking Pippin as the ring bearer, due to the fuckery with the palantir from Orthanc. When Aragorn gathers a bunch of volunteers for a suicidal assault on the Black Gate, Sauron thinks he's already power-drunk from the ring, and sends everything to assuredly crush them and reclaim it, leaving Mt. Doom almost completely undefended. His focused will alone is dangerous, and it's bent on Aragorns feint.
The eagles, even if they were willing to be steeds and pack ponies, even if they somehow had the provender to feed at least 12+ giant eagles, would have given the game away. Sauron had held back the Nazgul after they got wiped in a stuipid way because he was unsure where an all powerful ring bearer was going to show up, but the eagles would have made an obvious and easy target before they even entered Mordor, at which point they'd have Saurons 100% attention and awareness of their actual goal. So the witch king + the other nazgul + a shitload of orc archers and siege weaponry anti-air on point defense. Also I doubt the eagles fight as good with people clinging to them, neither would the fellowships fighting skills would be as effective except for Legolas maybe.