lord of the rings - Why didn't Isildur's Heir come forward sooner?

In Appendix A: Annals of the Kings and Rulers, we learn some things about Aragorn's family tree. There are basically two facts that together are confusing me:

1. The Kingdom of Arnor comes to an end in TA 1975 after the Dúnedain are basically wiped out battling the forces of Angmar. But the line survives in Aranarth, Aragorn's great-to-the-power-of-thirteen-grandfather.


2. The line of the Kings of Gondor comes to an end in TA 2050, when Eärnur dies with no sons and they can't find a pure-blooded Dúnedain to rule after him.

However, Aranarth is alive at this time (He doesn't die until 2106, meaning he's as good a candidate as any to take the throne of Gondor. So why doesn't he?

Showing my work a bit, the Appendix does give a partial answer. In 1944 the King and both his sons are killed in battle, and history tells us:

On the death of kind Ondoher and his sons, Arvedui of the North-kingdom claimed the crown of Gondor, as the direct descendant of Isildur, and as the husband of Fíriel, only surviving child of Ondoher. The claim was rejected. In this Pelendur, the Steward of Kind Ondoher, player the chief part.
[Arvedui objects to this on the grounds that he's still descended in direct line from Elendil]
To this Gondor made no answer. The crown was claimed by Eärnil, the victorious captain; and it was granted to him with the approval of all the Dúnedain in Gondor [...] Arvedui did not press his claim; for he had neither the power nor the will to oppose the choice of the Dúnedain of Gondor; yet the claim was never forgotten by his descendants even when their kingship had passed away.

So, okay. Maybe Aranarth (The son of Arvedui) doesn't come forward because he holds a bit of a grudge, or because he figures they'll reject him again. Fair enough.

But there are nine hundred years between when Eärnur dies and Aragorn takes the throne. For all of that time, we know that Gondor expects a King to return, and not just Eärnur himself:

Each new Steward indeed took office with the oath 'to hold rod and rule in the name of the king, until he shall return'. But these soon became words of ritual little heeded, for the Stewards exercised all the power of the kings. Yet many in Gondor still believed that a king would indeed return in some time to come; and some remembered the ancient line of the North, which it was rumoured still lived on in the shadows.

So everybody knows that Gondor is waiting for a King, and apparently the only people who don't know that the Northern Line is still alive and kicking is Gondor herself. So why, in those (again) nine hundred years, did one of them not come forward to claim the throne?