You forget one thing: The eagles aren't freaking vehicules, they are living beings with proud minds etc... The kind of "beyond elves" who are just as cool as they're willing to carry you out of trouble, and not into trouble, much like a friend who'd carry you home on his back after you've demonstrate your abilities to decorate a friends house with your own puke. I doubt they would just accept going into a suicidal mission for the sake of it.