Using Galadriel and Celeborn as main POV characters makes sense, when you consider that they traveled all over the place during the Second Age. Started in Lindon, then explored Eriador before settling down for a bit in Eregion. Galadriel decides to venture further east to Lothlórien while Celeborn stays behind. When Sauron's forces attack Eregion, Celeborn flees to Rivendell. After the War of the Elves and Sauron is over, Galadriel journeys back over the Misty Mountains and reunites with Celeborn in Rivendell. Then the two of them go south to Dol Amroth (which later becomes a fief of Gondor). So between the forging of the Great Rings, the War of the Elves and Sauron, making friends with the Númenóreans in Belfalas and Pelargir, and likely providing aid to Isildur and Anárion upon their arrival in Middle-earth, Galadriel and Celeborn had their fingers in many pies.
With that said, I don't know if I ever viewed either of these characters as fighters. Not in the literal sense anyway. I suppose that's the issue here. There's no elf in the Second Age that fills the "active protagonist" type of role. Elrond was Gil-galad's herald and bannerman. Gil-galad was the High King of the Noldor and likely did not participate directly in any conflict until the War of the Last Alliance. Glorfindel was basically the elf equivalent to an Istari, and was sent back to Middle-earth more to serve as an adviser than a warrior. Círdan basically never left Mithlond. Celebrimbor is... well, let's just say they can't build the show around him. And the Elves of Lothlórien and Greenwood the Great (Amdír, Amroth, Oropher & Thranduil) do not contribute much to the stories of the Second Age until the War of the Last Alliance, and even then they are very removed from the action (being on the eastern side of the Misty Mountains).
There's no clear-cut choice. Whereas with the human characters, there are choices aplenty.