I think that the entire matter just comes down to pride. Just as the heroes of ancient Greek plays usually were defeated due to their hubris, all these Elves' downfalls were through their excessive pride.
For example, Fëanor was a proud man. Deep down inside, he wanted to believe that he was perfect, that he was the greatest of the Eldar. He may have been such in his skill, but otherwise, he was not. That realization simmered bitterly in his heart. I think that also helped Morgoth "get to him" in the end. One of both Morgoth's and Sauron's weapons is playing on resentment. Fëanor kept driving himself to perfection, without listening to anyone, not even Nerdanel or his sons. And poor Fingolfin could only stand there and watch his brother destroy his own life and the lives of all those around him.
Ultimately, it was Fëanor's pride that led to the Rebellion of the Noldor and the Kinslaying. Initially, he refused to surrender the Silmarils to the Valar so that Yavanna could revive the Two Trees. But Morgoth stole them first. When Fëanor found out about Finwë's death, he went completely mad. He had no reason left in him.
Another good example is Celebrimbor. It was pride and a deep-seated desire for complete independence that led him to accept Annatar's councils when he knew that the latter had been turned away by Gil-galad. Perhaps I'm giving the High King more credit than he deserves, but I'm sure that he saw straight through Annatar the second that he started talking. Celebrimbor, on the other hand, was too much like his grandfather for his own good. He wanted knowledge, and he would have it at the cost of all else. His pride made him refuse to see that there was probably a reason for Gil-galad turning away Annatar.
I think it is unfortunate that in the case of the Elves, greatness was always tempered with pride. But then again, no one can be perfect. Fëanor would have been a great King, one that would have been remembered for all of eternity if it had not been for his pride. He is still remembered forever, but for all the wrong reasons.
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But Melkor also was there, and he came to the house of Fëanor, and there he slew Finwë King of the Noldor before his doors, and spilled the first blood in the Blessed Realm; for Finwë alone had not fled from the horror of the Dark.
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