The comparison of Arwen with Luthien is unfair, in that it doesn't take into account the role of elves in the Third Age as opposed to earlier ages. They are fading, and less directly involved in the battles of the Ring. Their role is to give aid and to hold down the "fortresses of goodness" they have established in Lorien, Imladris and the Grey Havens. If Arwen is a wimp, then so are Elrond and all the elves, save perhaps Legolas!
We can safely assume that Arwen is everything a great elven female would be, and that makes her a far sight grander, more noble, tougher and smarter than the stereotypical fainting female of epic literature. It's only if you're already assuming Tolkien's books are sexist that you would need "proof" of Arwen's liberated femininity.
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