Was it legit?

[Eonwe]

If that's the case, then Isildur's line does not have a claim to the throne.

I see no reason why Valandil shouldn't receive the High Kingship like his father would have.

In Appendix A, we find Arvedui's argument:

But when Elendil fell, Isildur departed to take up the high kingship of his fatehr, and committed the rule in the Sourth in like manner to the son of his brother. He did not relinquish his royalty in Gondor, nor inted that the realm of Elendil should be divided for ever.

It never says (here at least) why Arvedui's claim of the High Kingship is regected in Gondor. But it does say:

The claim was rejected. In this Pelendur, the Steward of the King Ondoher, played a chief part.

This suggests to me that there was some shady dealing going on. I think that Arvedui's claim is valid. And Aragorn's would certainly be valid, because the line of the King dies out completely, so he would be the closest with the highest claim to the throne.