Why didn't Frodo use the eagles to fly over Mt. Doom?

[Eothain Elfwine]

The eagles are entities in their own rights, not taxis. Perhaps like Elves they have their own worries and issues. Perhaps like Radagast they rarely come to that area of the world. On the whole they choose to do what they do when they do it. And probably flying a little creature called Frodo to the Dark Land was not one of the things they chose to do. Though they did pick him up afterward . . .