I'm not sure that you can make that case, especially when we're dealing with Elves. Even when there were cases where a king was killed, the throne did not necessarily go to his eldest son. For example, Feanor was the elder son of Finwe, but the throne went to his younger (and more rational) brother. The people of Gondolin looked to Tuor, a human and the king's son in law, rather than to a male relative of the king. And it doesn't seem that Elrond inherited any kingship, even though his father Earendil had been, basically, a king. I think the Noldor tended to chose the most suitable person as their king, and while it usually ran in families this was more because of the family having real worth, than anything else.
Anyway, after Gil-Galad's death, most of the Noldor looked either to Celeborn and Galadriel (who was Gil-Galad's aunt anyway) or Elrond, who was Gil-Galad's cousin by marriage. Maybe that's the reason why Elrond has Gil-Galad's ring... he was the closest, or most suitable, heir.
Yes, but he was an only child and out of uncles and cousins. It seems to me that he could have noticed that the list of heirs was growing thin.
Anyway, after Gil-Galad's death, most of the Noldor looked either to Celeborn and Galadriel (who was Gil-Galad's aunt anyway) or Elrond, who was Gil-Galad's cousin by marriage. Maybe that's the reason why Elrond has Gil-Galad's ring... he was the closest, or most suitable, heir.
Apparently they weren't up to the task, because the kingdom was no more. :)