Iām not sure whatās more scary. That this question was asked or that thereās an actual answer for it. š
@charlesgaba @RikerGoogling Also even if unopposed in the air, a single large squad of Orcs & Trolls could have defended or collapsed the one doorway to the fires of Orodruin / Mount Doom. Presumably Sauron himself could make them inaccessible on a moment's notice. Only deception/distraction allowed Frodo's access to be unnoticed until the last second.
Also, only a Hobbit could resist the corruption of the ring that long. It had ways to corrupt powered by the wearer's personal/spiritual power.
@DarlaDonna @charlesgaba @RikerGoogling
No doubt while we're joking about it there are srs academic papers on military doctrine in LotR somewhere out there. If not a whole community... if not yet, well, its only a matter of time.
I propose Rule 35 - everything online intersects eventually ;)
@DarlaDonna @RikerGoogling Or...
https://www.oglaf.com/ornithology/ (CW blood and gore)
The Nazgƻl didn't get flying mounts until after they were unhorsed at the ford near Rivendell. Had the eagles gone at that time, they couldn't have stopped them.
The real answer is narrative - it would have been a short and boring story. We can speculate a hundred retcons to explain it, but the reality is it would ruin the story. I favor the whole "not their business" explanation - they flew Gandalf and the rescue as a favor to Gandalf, but bearing the ring would be too much.
@RikerGoogling #TheEagles were more interested in playing #theJourneyOfTheSorcerer than participating in it, of course.

Provided to YouTube by Rhino/ElektraJourney of the Sorcerer (2013 Remaster) Ā· EaglesOne of These Nightsā 1975 Elektra/Asylum Records.Engineer: Allan BlazekRe...
The Eagles are very proud and powerful. Think āGwaihir the Ringlordā
Really long answer:
https://www.tor.com/2016/12/21/tolkien-eagles-manwes-special-ops/
@RikerGoogling https://www.oglaf.com/ornithology/
(This page SFW, others may not be and usually arenāt)