Indeed, given that other of the
Maiar (called
Wizards) were sent not to directly participate or use their powers, but to "aid the
peoples in their fight", this thoroughly explains why the
eagles "didn't just fly
the ring to
Mordor." It was not their charge - any more than it was for
Gandalf to directly confront
Sauron.
Gandalf confronted
Saruman as he was behaving contrary to his charge - he had broken the charge by trying to grasp and use power directly, and for his own ends. But note Gandalf waited to do so, until the "peoples of
Middle-earth" (the
Ents in this case, though this is perhaps disputable on two levels), had turned the tide against him utterly.
And of course the
Balrogs were as out of line as was Sauron. (And
Melkor, though a
Valar, before him.) Thus Gandalf was at liberty to deal with the
Balrog at the bridge - as indicated by his "“
Fly! This is a foe beyond any of you. I must hold the narrow way. Fly!”
But there's an added reason Gandalf could confront the Balrog directly... the
Istari were to 'aid the free peoples' and it was the 'free peoples' at the
Council of Elrond, who determined the
Quest of the Ring to return to Mount Doom. (Note Gandalf's interplay in that whole Council. The decisions were not made by or left to him at all.) So the overriding concern with Gandalf's direct involvement with the Balrog, was to 'enable the decision of the Free Peoples in how to resolve the conflict regarding the
War of the Ring." He was not a decider, but just a piece of the puzzle in insuring the Free Peoples were able to conduct the war.
Once again
Tolkien demonstrates his depths in insuring both "religious and moral elements" and integrity are maintained, 'but not overtly', throughout his works.
ADDED NOTE:
We see this same played out again and again throughout Tolkien's works.
Gandalf acts as information provider, clarifier, counselor, but never decider.
When
Bilbo is letting go of the ring.
When the
Great Eagle takes them to the Carrock rather than to Mordor. (The decision of going to the Carrock not made by Gandalf.)
When the decision is made to try Carhadras, then again when the decision is made at last to go into
Moria. Both made by the people, Gandalf counseling.
When
Frodo decides to take the ring, it's
Elrond advising 'it seems to be the path chosen for Frodo' not Gandalf. Gandalf simply responds "i will help you with this burden as long as it is yours to carry."
Even in the decision to go to
Helm's Deep Gandalf is not the decider, but a counselor, and once decided, a gatherer of troops to help.
No, there is no
mystery about why the Eagles didn't take the ring to Mordor.
They simply could not. Iit was not "the free peoples' choice" at any time.
Sorry, I've a new and consistent 'triad of
events' opening out before me, circumstance and event after circumstance and event, seated very deeply in Tolkien's planning since the beginning of it all, unfolding in my mind.
This Triad will be brought into focus fully, in my Middle-earth book. I had not seen it in quite this way before, but it is a solid connector between circumstances, events, people,
places, things, morals, religious inclusion, and more.
Frodo's final events at Mount Doom as he claims the ring and
Gollum at last plays his part Gandalf had somewhat foreseen, fit into the Triad.
Whew... I'm suddenly mentally exhausted.