The Winged beasts vs The Eagles

The battles fought in the North were of far less importance to Middle Earth than the survival of Minas Tirith. The scale of the army heading from Mordor to Gondor would also have been far greater than anywhere else. Plus we add the fact that the Eagles had already appeared in the Battle of Five Armies of their own accord. They would have served as an excellent shield to fend off the Nazgul if deployed by Gandalf. He would have had plenty of time to send messengers to gain the support of the Eagles. They are also loyal to him when called.