My contention is that there is nothing in the text to rule out such a plan, and that it is simply a hole in the plot of an otherwise excellent book that the issue is never brought up. This is not to say that LoTR is in any way a bad book; it merely shows that even as excellent a writer as Tolkien does not always succeed at perfectly harmonizing the various entities which he has placed in his world. As Tolkien himself says,
Could the eagles have flown Frodo into Mordor?
Sean Crist investigates a major plot hole in the Lord of the Rings.