In the interest of thoroughness, I reread the Council of Elrond. I think the choice to hike it there was borne out of the need to remain as hidden as possible, as there were things monitoring the air as well as the land, and by the time they left the nine riders had become the nazghul, and thus the eagles may or may not have succeeded, and Sauron's attention would have been on them anyway. With the company split, and Frodo and Sam on the ground, the rest of the Fellowship could distract Sauron sufficiently for Frodo to make it to Mount Doom.
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