Perhaps "cut and run" was a bit of an oversimplification of what cantbebought was saying about Gil-galad not having an heir.
He ruled for 3,514 years and marches off to the biggest war in ages were, when he falls, the Noldor Kingdom in exile also fails.
Isn't producing an heir part of a king's (let alone a so-called High King's) duty? So when he "cuts and runs' on his dynastic duty, it was history for the Noldor Kingdom in exile.
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.