It was mentioned before that the Eagles would likely be killed by the Nazgul if they were to fly into Mordor, but the Eagles could have perhaps dropped them off some where even if they only took them to Lorien.
I believe that the Eagles didn't fly the Fellowship anywhere because if they had LOTR wouldn't be LOTR.
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"One more soldier dies, and when he gets to Heaven, to St.Peter he will tell, one more soldier reporting for duty, I've served my time in Hell."
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