[Formendacil]

Personally, I hold to the theory that the Eagles carrying Frodo to Mordor would have been WAY too obvious...

Not from a storyline point of view, but from and in-story point of view.

The Eagles, you know, are pretty conspicuous creatures. Any sighting of them tends to herald something big. So Sauron, who's eyes are constantly scouring the West for signs of suspicious activity (like Aragorn...), and whose Palantír handily solves the problem of limited sightrange, would most likely have seen the Eagles coming.

What then?

Well, even the Eagles take a certain amount of time to go from Point A to Point B. Sauron, who certainly would have had Rivendell at the top of his "to watch" list at the time Frodo was there, would have noticed almost immediately if the Eagles had picked up some passengers, and headed straight to Mordor.

Sauron, who was in a corporeal form, and more than able to move and fight (contrary to what PJ would have us think...) would certainly have time to get to Orodruin, and camp out there.

And even without the Winged Nazgûl, there were undoubtedly several ways in which Sauron could attack a flying eagle. But even if there wasn't, he could just wait at Mt. Doom until Frodo, Gandalf, and the Eagles showed up.

What then?

Well, since Gandalf was still Gandalf the Grey, and had not yet received his greater mandate as Gandalf the White, he probably would have died. After all, the Balrog got him, and Sauron was a lot stronger than the Balrog. Meanwhile, all it takes is a host of orks to keep Frodo occupied (or even just a big boulder in front of the entrance) so that he can't drop the Ring in.

With Gandalf and any other companions dead, Sauron can now turn his full attention to Frodo. Face to face, the Ring wanting to return to Sauron, is there any doubt what would happen?

Sauron would regain the Ring.

Remember, the great strength of Gandalf and Elrond's plan was it's utter foolishness. The reason that was so successful was that it meant that it was an IGNOREABLE thought, and so Frodo and Sam were able to SECRETLY sneak into Mordor. Eventually, Gandalf even went so far to aid this secrecy that he risked pretty much half the military might of the West in a suicidal march on the Morannon.

The Eagles aiding the Battle at the Morannon was therefore an asset at this point, since it added to the spectacle and likely helped keep Sauron's attention on the West. As for the Battle of Five Armies, there was no Sauronic threat at the time, nor was there any reason for secrecy.

That, basically, is my opinion.