Are you implying the eagles are Valar? What you say about the Valar intervening is true but the eagles are mortal beasts. The reason I’ve heard most often is that eagles are not stealthy enough, Sauron would see them coming and counter them with fell beasts, nazgul, archers, siege engines etc. This kind of assault is exactly what Sauron expects from someone who just claimed the ring for themselves and what he is prepared for. Gandalf stresses that the quest relies on secrecy and stealth. If the eagles going to war would wreck middle earth, wouldn’t it have happened during the battle of the five armies? Or at the battle of the black gate?