Tolkien's 'Deus ex Machina'

[Boromir88]

There are certain situations when we see Tolkien use the authorial device of 'deus es machina' to help out our heroes from problems. It translates to 'God of the Machines' which means that some supernatural power/being/creature comes into the story to help our heroes out of a sticky situation, or solve the plot entirely. And Tolkien does use 'supernatural forces' on several occasions in his story.

For example, he admits the Eagles are 'machines.':

The Eagles are a dangerous 'machine'. I have used them sparingly, and that is the absolute limit of their credibility or usefulness.~Letter 210

Also, there are times when Eru sticks his hand into things and gets involved. For instance sending Gandalf back:

He was sent by a mere prudent plan of the angelic Valar or governors; but Authority had taken up this plan and enlarged it, at the moment of its failure. ’Naked I was sent back -- for a brief time, until my task is done.’ Sent back by whom, and whence? Not by the ’gods’, whose business is only with this world, for he passed ’out of thought and time’~Letter 156

And indirectly destroying the Ring:

Frodo deserved all honour because he spent every drop of his power and will, and that was just sufficient to bring him to the destined point, and no further. Few others, possibly no others of his time, would have got so far. The Other Power then took over: the Writer of the Story (by which I do not mean myself) 'that one ever present person who is never absent and never named' (as one critic has said)~Letter 192

So there are a few occasions that we see Tolkien using 'deus es machina' in his story. Now the question of debate is this has often been a cause for criticism against the books. It seems rather 'cheap' to solve situations with supernatural powers. Is it a quick and easy way out? Does it drag down the story and actually make it a weakness? Does it make Frodo's journey seem almost completely useless since all Eru had to do was take control and have the ring destroyed?

Or does Tolkien actually use 'deus es machina' to a great effect and able to serve a purpose in the story? What I mean here, is to examine the why. Why is there a special significance in using 'deus es machina' at certain key points throughout the story? Is there even an importance? We know he uses it, but the bigger question is why does he use it? And if there is an importance what is it?

I have some ideas that I've kind of put together, but I want to wait and here some responses to get the discussion going. So...umm...have at it.