You missed the whole point. He helped her stop being a little girl and transformed her into a cold-blooded killer. He never stopped being a name on her “list”, but ironically, like all the others on the “list” who’ve died, she hasn’t had to do any of the killing herself.
I loved Arya in that scene. Just staring him down, despite his obvious attempts to anger her and provoke her into stabbing him, she just... watched. And left him to die.
Taking the money pouch was both practical and a last dig at him for the money he stole from the farmer he robbed a few episodes back.
She did stick that one guy a few episodes back--and she cut the throat of the guy at the campfire.