I enjoyed the thought and analysis that went into this post. It might not be a satisfying answer, but the conclusion seems to be that Tolkien didn't think about eagles as a likely course of action. And if he did, he didn't bother to address it.
It's funny to think that we'd never have this conversation if there had been a line like, "for Sauron can sense the great power of the eagles as they approach Mordor." The fact that fans long for "canonical" answers when there are none is a testament to great writing.
Certainly a very interesting analysis, whenever an author uses a deus ex machina, people are bound to come up with explanations, criticisms and the like. Here though it seems like an attempt to you know explain with an inherent internal logic of the Middle Earth.
Agree totally that it is a very great piece of writing.
It's funny to think that we'd never have this conversation if there had been a line like, "for Sauron can sense the great power of the eagles as they approach Mordor." The fact that fans long for "canonical" answers when there are none is a testament to great writing.