Could the eagles have flown Frodo into Mordor? (2000)
As the article points out, it's a question of stealth versus speed, but speed is not necessarily preferable. The powers of Sauron, especially deep within his own domain, are indeed unknown. With even an hour to react, it is quite possible he would be able to conjure up something that would end up in the whole endeavor delivering the ring to him, instead of destroying it. On the other hand, the stealthiness of hobbits is well familiar to Gandalf from his previous experience with having Bilbo as a "burglar", and there are various things that the allied forces can do to further distract Sauron's attention. The power of the eagles is also something that Sauron knows and fears, and that he probably took precautions against; whereas hobbits are creatures that he most likely underestimates.