Why DIDN'T they just fly the great eagles to Mount Doom?

Before someone says they would have been caught or shot down, did you SEE how many of them there were, and it wouldn't be that hard to fly at night and get past any defenses they may have had. plus if you just fly to Gondor, load up all the great eagles with archers and rocks, now you got yourself a nice little air raid, and all you need is to get 9 or so (the ones carrying the main party) past the defenses and you've pretty much skipped the WHOLE defensive ground perimeter of Mordor.