Arwen doesn't have any characteristion at all in LotR. It's not just that she isn't a warrior - she isn't anything! Who is she? We don't know. She might not be useless, but we have no infomation. We're told she's beautiful, but that's all. We only know her as somebody's daughter or somebody's betrothed. Even including the Appendices we know next to nothing. Arwen is mostly an unknown because
Tolkien decided that her character did not merit further development.
I have no problem with that. You can't give full backstory and motivation to every minor character (and that is a separate issue than the lack of female characters in LotR). But I do have a problem with PJ making Arwen into a Big Deal, and (for example) usurping
Glorfindel, who is a far more prominent character in canon, just for the sake of a 'love interest'. I think PJ said in an interview that writing out Glorfindel was a good decision because he only has a brief appearance, but you could say the same about Butterbur or
Celeborn. In fact, Glorfindel is more crucial to LotR than Celeborn, so it makes absolutely no sense at all that he was written out in favour of barely-there Arwen.