Elrond and Sauron, a personal vendetta?

[Elmo]

I can't imagine why Celeborn would not fight against Sauron in the alliance especially after his role in Eregion. Elves stay able to fight all their life so it would make to try and take all your strength to Dagorlad despite him personally not having an army behind his back. I doubt they marched with the Wood Elves because surely Celeborn would have been able to prevent Amdir's suicidal charge he is called the Wise for a reason. Or maybe Amdir just ignored him!