Galadriel

They aren't important in the story.

Only, what, three or four 3rd Age Noldor are ever mentioned by name? Gildor, Galadriel, Glorfindel, whatshisname Erestor(?) at the Council... any more? If a descendant of Gil-galad isn't going to be the King, he's probably not taking an active role anywhere. Maybe the guy who bakes Gildor's bread is Gil-galad's son.
 
I’m not arguing against those conclusions but let’s not forget that Tolkien recycled or ‘borrowed’ names from his own stories without necessarily connecting the new story to the old. In the beginning, Tolkien probably wasn’t connecting the world of LOTR and the Hobbit with the Silmarillion, that happened during the writing process. So when he wrote about Gildor Inglorion, he didn’t think of him as a descendant of Finwë but just gave him a name he found appropriate. I don’t know why he left it after connecting the worlds of his stories (that goes for other stuff as well of course, like the Gondolin swords etc) but after all, he had no hopes that the Silmarillion would get published and who knows what changes he would have made if that would have happened during his lifetime.
 
Cool.

And I like to think that the Noldor who are around just all instinctively know this. Like, Elendil and Gil-galad are freshly dead. Isildur takes up his kingship on the battlefield, turns to Elrond, asks who will be the next Noldor king. Elrond looks at him, confused. "What do you mean, next king? There are no more Noldor kings on this side of the sea."
I don't think Elrond ever identified as part of the Noldor he saw himself as more Teleri.

Without much evidence, I have always felt there are 2 main reasons why the Noldor had no king after Gil-galad.
1. Lack of Elves
2. Elrond refused the job

I think both the Sindar kings and the Noldor would have been quite happy for Elrond to claim a High Kingship, but for whatever reason he didn't.
 
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