[A_Brandybuck]

I think, that the real question concerning the eagles is not, if they would make it to fly to the Orodruin with Frodo and the Ring, but if they are allowed to interfere in the events of Middle-Earth.
It has been often posted, that the Eagles are the messengers of Manwe in Middle-Earth. Consequently they are under the control of Manwe. But we know, that the Valar, of course including Manwe, sent the Istari to Middle-Earth to assist the Free Peoples of Middle-Earth in their fight against the Dark Lord Sauron.
But the Valar didn't send the Istari to lead the Free Peoples of Middle-Earth against Sauron and consequently play the main-role in defeating Sauron. So why shouldn't the same rules count for the Eagles?

When the Valar wanted the Eagles to play a main-role in freeing Middle-Earth, why did they make the efforts that the Istari were diminished in power and their mission had only supporting character?

But flying with Frodo to Mount Doom means exactly taking a(the) main-role in defeating Sauron.