Good points. Unless Gondor changed its succession law after the fall of Arnor(and there is nothing I’m aware of to suggest they did), Aragorn has no claim to their throne. By the time Aragorn arrived in Minas Tirith, there were probably dozens, at least, of people with a much more recent relation to the last king of Gondor.
Aragorn might have been able to make a claim to Arnor, saying that the line of kings long absence from actually running things was more akin to a government in exile than a tacit abdication, or that when the last king abdicated his successor would immediately be king. But Gondor? No.
That said, it still might have been done. There’d likely be a few nobles that would complain about the breach in succession law, but I could see the Gondor parliamThe Toast’s Middle-earth correspondent courts controversy as he explains why Aragorn’s claim to the throne of Gondor was shaky at best.
ent or cabinet or whatever similar body going with Aragorn.
While there would be some people with a closer link to the previous dynasty, we don’t hear about them. It seems unlikely they’ve shown major leadership potential or otherwise qualified themselves as king in anything but bloodline. And here’s Aragorn. Blood claim to the throne vanishingly weak, but he shows up as Minas Tirith is about to fall. He gets the immediate situation stabilized with respect to civil order. He rallys Gondors army, and brings in thousands of reinforcements including a literal angel. He successfully holds the line against the forces of Sauron until the One Ring can be destroyed and the war decisively won.
OF COURSE Gondor would make him King, with the remaining legitimate authorities making whatever legal changes they have to to make it happen.
Oh, who would have been the chief executive had Aragorn not claimed the throne? The Steward. Faramir. Who was alive at the time. I’d expect his opinion on whether or not Aragorn should be King would carry a lot of weight, and possibly even the force of law to some extent.