Another thing...Why did the elves not fight?

[Eomer of the Rohirrim]

The Elves did fight. In fact, they had been doing little else for thousands and thousands of years.

[Maédhros]

But the Elves did fight.
From LOTR: Appendix B: The Tale of Years

After the fall of the Dark Tower and the passing of Sauron the Shadow was lifted from the hearts of all who opposed him but fear and despair fell upon his servants and allies. Three times Lórien had been assailed from Dol Guldur. but besides the valour of the elven people of that land the power that dwelt there was too great for any to overcome, unless Sauron had come there himself. Though grievous harm was done to the fair woods on the borders, the assaults were driven back; and when the Shadow passed, Celeborn came forth and led the host of Lórien over Anduin in many boats. They took Dol Guldur, and Galadriel threw down its walls and laid bare its pits, and the forest was cleansed.
In the North also there had been war and evil. The realm of Thranduil was invaded. and there was long battle under the trees and great ruin of fire; but in the end Thranduil had the victory. And on the day of the New Year of the Elves. Celeborn and Thranduil met in the midst of the forest; and they renamed Mirkwood Eryn Lasgalen, The Wood of Greenleaves

It is a common misconception that people have that the Elves didn't fight at all. Remember that Sauron had forces in the North of ME (Dol Guldur) and the Elves who mostly dwelt there had to defend themselves. If they were to go (as the movie does) to fight in the south, who would have defended their own realms?