Interesting theory, however, is there any example where the eagles come to the last minute rescue of Sauron's forces in order to maintain the balance of power?
Eagles are seen only as messengers of good. In general that would be a question only from the perspective of dualism, but I don't think this is the case with the Tolkien's view on his world. The world appears predominantly evil, but in essence Tolkien maintains the view of the ultimate good (i.e. hidden), as an intention of Eru. So tipping the balance into the good side usually doesn't disrupt it as much. However extreme shifts still can have serious consequences. Valars getting involved in banishing Morgoth destroyed Beleriand altogether. The fall of Sauron diminished the Elven presence and so on.
