[Elladan and Elrohir]

This discussion is intriguing, though it has strayed far from its original topic (as threads often do).

Regarding the legitimacy of Aragorn's claim to the throne, I point out again that his claim to the throne was as the Heir of Elendil, not as the Heir of Isildur. He was the only man on Middle-earth who could inherit any of Elendil's rights and properties. I would also add that, though it makes little difference, he was descended from Anarion as well as Isildur, for Arvedui had wedded Firiel, daughter of King Ondoher and a direct descendant of Anarion.
I would also add that the Council of Gondor likely was a sort of Supreme Court, where decisions might be made and then overturned. Obviously, allowing Aragorn to become king overturned the decision against Arvedui way back when. So Aragorn's kingship was not illegal in any sense. Not to say that anyone on this thread has said that, but it seems to be implied in some cases.

Of course, one may fire back that I have a vested interest in defending Aragorn's right to the throne, since he is one of my favorite characters in Tolkien. This is a genetic fallacy, but it is sadly also true. With that, I leave you.