You forget about the fell beasts. Those are the flying reptiles that the ringwraiths rode after their horses were washed away in the flood at the Ford of Bruinen, outside Rivendell. The Eye would have spotted them many leagues away, and sent his fell beasts to intercept them. The eagles would have been torn to pieces long before they reached Mordor. The only reason the eagles were able to rescue Frodo and Sam after the destruction of the One Ring was because Sauron could no longer control the fell beasts. It's also why Aragorn and his army survived the battle at the Black Gate. Sauron could no longer control the orcs, trolls, etc., and without their dark master's presence, they fled.
I know, your post was made in jest, but there are some who actually hate LotR because of this supposed "plot hole" that is easily explained with just a little thought.
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