The real reason is Christianity. Basically, because of stuff from earlier in history, Middle Earth is basically "fallen," though "god" is still active there in some way, "god" (Illuvatar) and the "angels" (the Valar) are in some ways cut off from the mortals. The Eagles are the servants of Manwe, the chief Valar. Like in (some versions of) Christian theology, God doesn't just save you; you have to try your best to do all that you're supposed to do (follow the commandments, receive the sacraments, etc.). This is not enough though, you still need grace to be saved, there's some verse I kinda remember that's like "it is by grace we are saved, after all that we can do." Middle Earth has to deal with the problem of Sauron. Were the Eagles actually willing to just fly them to Mordor, it wouldn't have even reached that point cuz they could have just shipped the ring over the ocean to Valinor, or the Valar could have just invaded Mordor themselves. And Frodo needs to try his hardest to achieve the task appointed to him. Of course, none of this would have been possible without some guidance from "god" (Gandalf is basically an angel, for example). And even at the end, Frodo's mission would have failed had not Illuvatar intervened to make Gollum fall into the fire, and also Frodo would have died in the eruption afterwards. But because him and Sam endured to the end to the best of their ability, they get grace and are saved by the Eagles.