You need to look at the geopolitical situation in Middle-Earth at the end of the Second Age.as you follow the dynastic fights between the Noldor (High-Elves) you wonder: who is the rightful "High-King" (overlord of all Noldor) after Gil-Galad died?
apparently, the elves were so weak after the War of the Last Alliance that they just didn't bother having one again.
Numenor had taken Sauron prisoner, and under his influence man attacked and invaded the Undying Lands. The Valar destroyed Numenor, and made the world round, and now what was left of the elite of humanity had settled in Eriador and along the banks of the Anduin. Sauron had escaped back to Mordor, and he had raised an army to destroy the last of humanity. And when Isildur had a chance to destroy Sauron and his evil forever, he stepped back from that brink.
For the Elves that were left in Middle-Earth, there was no longer any reason to stay. Their leader, Gil-Galad, was dead. They had suffered heavy losses in the War of the Last Alliance for, ultimately, no reason. Sauron had suffered a defeat, but it was only a defeat. Sauron's evil was going to rise again, and based on past experience, man was susceptible to Sauron's corrupting influence. Man would grow in population and strength, and eventually Sauron would strike. Tolkien's Elrond would not have been as fatalistic as Jackson's Elrond about humanity's chances in a struggle against Sauron, but there was no reason for the Elves to fight and die for what would be, in all likelihood, a opeless cause. The Elves had an escape route, and it's one they took, until eventually they were isolated communities. They had no need of a High-King, when the individual communities were on their own.
Yes, this is a gross simplification, and the Elves weren't entirely uninvolved. They did drive Sauron from Dol Guldur at the time of The Hobbit. But they didn't do that for humanity's benefit; they did it because Dol Guldur's power threatened Lothlorien and Rivendell.