Do you really want th answer to that?
The great and powerful cannot wield the ring (that's why Aragorn doesn't go with Frodo and why Gandalf never picks it up). Just as Frodo couldn't in the end, they could not have droped it in the fire.
So, why didn't Frodo fly on the wings of eagles? Because the eagles would have taken it.
Oh, and one must presume that Sauron would have been pretty good at spotting half a dozen eagles flying in towarRAB Mt.Doom!
Yes its sad that I knew this, but not as sad as you not knowing it!