@brion I'd like to think that explains everything. But theni try to think like a tactician, and I wonder... Eagles have to be everywhere, right? Is Sauron destroying all eagles on sight, on the off chance that one of them is probably carrying a Hobbit who happens to be a ring bearer?

Even thinking that there could be a risk there, wouldn't it still carry greater odds for success than wearing the damn thing while trekking on foot across half the planet and walking into a volcano?