Worthy contribution, BW
In the Third Age, there were actually not many Elves left in Middle-earth, and just one Kingdom, which was Sindarin, not Noldorin (actually, it was an Avari Kingdom with a Sindarin ruling family, IIRC). The other realms were just rather small groups of Elves living together around the Grey Havens, Rivendell and Lothlorien.
For having a High King, there has to be other Kings amongst whom he is the foremost. As there were no Kings left after Gil-Galad's death (except for Thranduil) there was no need for a High King.