I seem to remember the Eagles (take it eeeeaaaasy, take it eeeeaaasy...okay, sorry, I'll stop now) seeing most of Middle-earth the way Elves saw Men: nah, we have our own world, we don't really want to get involved in your affairs and risk stuff. But it's been a while since I've read The Hobbit
I do think the Nazgul would have been the biggest deterrents to a Ring-carried-by-Eagles mission - they're kind of Sauron's personal air force. Not only is the point of the story that
even the smallest person can change the course of the future, but that sometimes it's
necessary for the smallest person to be the change while the eyes of the wise and mighty are elsewhere.
It's always my friends who aren't too keen on Tolkien who insist that the Eagles should have dropped the Ring off at Mount Doom and spared them nine hours, anyway