I suspect Arwen spent much of her time working as a diplomat and councillor to her father. This is not stated explicitly in the text, but considering the situation at Rivendell, and Arwen's travelling back and forth between Rivendell and Lorien, it seems likely. Her mother was gone, her brothers don't appear to have spent much time in Rivendell, as far as I can tell, it was Elrond, Glorfindel and Arwen keeping the place going, and Arwen maintaining the alliance with Lorian.
I can see the use of the knight-errantry of Elladan and Elrohir, but I think the work of Elrond, Arwen, Glorfindel and others was even more important. Elves had a safe haven in the west, they had only to succumb to the sea-longing to leave all problems behind: threats, danger of capture, torture, etc. It can't have been easy maintaining Rivendell as a haven and persuading a critical mass of elves to resist the lure of Valinor and stay in Middle Earth with all its darkness and dangers, slowly fading all the while.
Galadriel was still concerned with the fate of Middle Earth, but Lorien appeared by the time of LotR to have largely if not completely cut itself off from non-elves. I think Arwen served a crucial function as a diplomat, maintaining communication and alliance between the still-powerful but increasingly inward looking Lorien and the resolutely outward-looking, welcoming and hospitable Rivendell.
I've never believed in the movie Arwen hurtling around by herself on a fast horse, because considering what happened to her mother, the relentless worrying would have caused Elrond to implode into pulverized pixie-dust. It would have been too cruel, even for the sake of Eowen-style shieldmaiden self-actualization. Even in company with a troop of armed elves, it can't have been easy for Elrond when she travelled, but they both handled it.
While not as dramatically correct as knight-errant or shield-maiden, I think the work of a diplomat and ambassador is just as important, if not more so. It was after all Gandalf's role as well for virtually all of his time in Middle Earth, would you call him a purely ornamental sex-object?
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