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,
Sean Crist investigates a major plot hole in the Lord of the Rings.
The Lord of the Rings book covers designed by J.R.R Tolkien himself.