It is not the magic of her people or of the land, it is the magic of her father. I felt it was important to the story that Elrond was a badass himself and that it was HIS protection that kept them safe. Yes elves are powerfull, but there are only two who are that powerful: Elrond and Galadriel and that is because they each wear a ring of power. The power of the land of Rivendell and Lothlorien is derived from the rings, and the reason that Lothlorien will die is not because Galadriel will leave but beacuse her ring will lose its power when the one is destroyed. Gandolf has the third but it is unclear whether his magic is because of it or his heritage. It is possible to have Arwen be a strong character without this. Would it have been so bad if she had called out "Father we need your help" or something similar.