One-Winged Balrog

I thought the Eagles had only arrived for the battle, to fight the Nazgul, but you may be correct, too.

The Aeneid is totally a fanfiction of the Iliad. Actually, 90% of ancient Greek and Roman literature is just a pile of fanfiction.

Or perhaps Tolkien just really liked the Just In Time trope.

Was the significance of exact timing in the denouement of The Lord of the Rings plot discussed somewhere? Perhaps by Tolkien himself in letters somewhere? I'm talking about Frodo and Sam arriving at mount Doom precisely as the Host of the West engaged the army of Sauron in an unwinnable battle. Were Frodo and Sam to arrive a day later, and Gandalf, Aragon, Éomer, Gimli, Legolas and Peregrin would all be dead. Eagles would also be either dead of dispersed, and assuming the ring still gets destroyed, Frodo and Sam would also perish. Were Frodo and Sam to arrive a day early, there would be no climactic confrontation at the Black Gate... but assuming the ring gets destroyed, Frodo and Sam would still perish, because the Eagles are nowhere near.

So, I remember dropping the first book because none of the characters were relatable. Does it change at some later point? Is there anyone to empathize with?

You people are all missing the point. It is not Elves, nor Ents, nor the Gondorians who are the paragons of Middle Earth, but hobbits. And they have a democracy, albeit a very small-government farmer-libertarian one. It's a contrast between what Tolkien liked in myths and legends (ancient kings of divine bloodlines, blah blah et cetera) and what he liked in real life (the Shire).

Humans in LOTR just haven't advanced enough to accept democracy. As opposed to hobbits, who need no divine blood to elect Sam Mayor of the Shire for seven consecutive terms.