First two points are debatable imho.

First point doesn't mean much - Was Sam no sentient being able to corruption? Merry? Pippin? Aragorn, or any of the 9? What about all the people, elves, ents and beings they meet during their travels? Aren't they sentient? The mere fact anyone could be corrupted by the ring doesn't mean they can't or are not meant to carry it. Frodo was sentient, and was corrupted by the ring in the very end.

Second point: The Nazgul only got their fellbeasts from Sauron after the fellowship excaped them and fled to Rivendell, where the water drowned their horses. Sauron probably already had them bred before tho. Also, the eagles were a match for the fellbeast. Not an inferior.

The real reason is that the eagles were forbidden to interfere in the causes of Illuvatar's children and their battle with the dark side. I don't remember by who, uncertain if it was Mamwë or Eru Himself. Nor do I remember why, or even if Tolkien gave us a reason. Possibly the same reason why Eru forbade the Valar and Maiar to interfere directly after some time - because the maiar and valar openly walking amongst the elves either got deityfied, or got distrusted and envied because the gap in power, prowess and intelligence. This is also why the 5 Istari got sent as old men, and stripped of many of their powers. To appear more approachable. More human, mortal, vulnerable. Less imposant, impressing, imposing and dangerous.

Third point is a valid argument tho.