Evidence for theory 1 indicates that in the book they did help Aragorn in the battle of the Black Gate and take down some of the winged Nazgul. A "dog-fight" with Frodo on their backs would most assuredly end in a Sauron victory.

Theory 2 comes from speculation from Tolkien (ie: he hadn't fully decided yet) that they were Maiar, or primordeal spirits, sort of pseudo-gods. Sauron was one before he "fell", and Gandalf and the other wizards are others. Like most gods/spirits in other religions the Maiar's power is bound up in following the orders of the Valar, who were the creators of the world.

In that sense, saying "Why didn't the Eagles drop Frodo in Mt. Doom" is akin to asking "Why didn't Moroni just hand Joseph Smith an English translated copy of the Plates. It would have saved us a lot of trouble." Moroni definitely COULD have done just that; however, it doesn't work that way. Events in the world need to progress by the deeds of those who are mortal. Same case with the Maiar.

At the end of the day, Tolkien said:

"The Eagles are a dangerous 'machine'. I have used them sparingly, and that is the absolute limit of their credibility or usefulness."
— J.R.R. Tolkien on flying the One Ring to Mount Doom"


Take your pick on either theory....I prefer theory 1 myself. Tactic wise, it would be stupid to sent Frodo into Mordor on the back with the ring. The movie would have been 15 minutes long and the bad-guys would have won. .