[alatar]

The eagles were permitted, in my view, to enter the fray as the quest was finished. To show beforehand (excepting the dwarf and wizard airlift to the vales of Anduin, of course) would be breaking the rules. Eru, through Manwë, sends the Istari to counter Sauron. Surely if it wanted a faster result, though with little to no free will input from the ME dwellers, Eru could have permitted the Istari Uncloaked to be delivered to Sauron's porch via the Eagles. Sauron may be the match of one or two wizards, but not five at once, and not as wizened old men but as they are in Aman.

But where's the fun in that? That would be like me pre-chewing all of my children's food. Sure it would be fun, but they'd develop weak jaws, and exactly why would they need teeth? And when I'm gone...

So the Eagles get to show up after the residents of ME, acting together (the feint of Aragorn, the defense of the Mark by the ents, the Galadhrim and Bardings etc etc) along with Frodo, uproot the current big bad weed. They're a bonus. Frodo and Sam could die on Mount Doom, but they're still needed to start the cycle again, as we see in the Scouring, as most likely the Valar aren't sending any more help.

Sauron is defeated and the rules aren't broken.