Okay, you caught me.

But Arwen did take the reins (since there weren't any reins when you're riding bareback, but you get the point) when she rescued Frodo from the Wraiths and rode him to Rivendell. That whole chase scene reminded me very much of Xena.
Having said that, I can understand why PJ did it. Glorfindel isn't really as important to the movie as Aragorn's love interest, which is why she got his part. I just don't think his choice for expanding her role was appropriate.
And you're right, Eowyn didn't technically fight
alongside Aragorn, but she did fight.
And thanks Enca!
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Most likely to die tragically: Aragorn
Most likely to die amusingly: I agree, poor Pippin