Tolkien scholar Michael Martinez examines the question of whether the line of Númenorean kings and queens expired with the destruction of Númenor in the Akallabêth and the vanquishing of Ar-Pharazôn and his great fleet.
It’s also a nice little history lesson for those interested in learning more about the heritage of Arnor and Gondor, and Aragorn’s forebears.
Was Elendil the Rightful King of the Númenoreans?
No. Ar-Pharazôn was the last King of the Númenoreans. His queen, Ar-Zimraphel (aka Tar-Míriel) was the last rightful ruler of the Númenoreans by inheritance.
When Númenor was destroyed by Ilúvatar its legal existence and the line of its kings came to a lawful end. The survivors of Númenor were bereft of kings and lawful rule, except in that the various colonies may have retained their local governments. The cities that were included in Elendil’s realms must therefore have foresworn their own independence in favor of his rule.
The last leaders of the Faithful, Elendil and his sons, escaped from the Downfall with nine ships, bearing a seedling of Nimloth, and the Seven Seeing-stones (gifts of the Eldar to their House); and they were borne on the wings of a great storm and cast up on the shores of Middle-earth. There they established in the North-west the Númenorean realms in exile, Arnor and Gondor. Elendil was the High King and dwelt in the North at Annúminas; and the rule in the South was committed to his sons, Isildur and Anárion. They founded there Osgiliath, between Minas Ithil and Minas Anor, not far from the confines of Mordor. For this good at least they believed lad come out of ruin, that Sauron also had perished. (Source: “THE NÚMENOREAN KINGS”, Appendix A to The Lord of the Rings)
Elendil’s reign as High King of the Númenorean Realms in Exile and High King of Arnor begins in Second Age year 3320, the year after Númenor’s destruction. Hence, his kingship begins a new lawful dynasty of which he is the progenitor. That is why Aragorn declared himself to be “Elendil’s Heir of Gondor” when he visited Edoras with Gandalf, Legolas, and Gimli. He was never anyone’s “Heir of Númenor”.