Except Frieren has never been one to initiate a fight against human even if said group of human has a mage killer. For one thing, she put tracking magic on the coin for precisely that, "tracking" and even went so far as to mask the magic so her purpose in the first place was clearly not to kill. Also, her current task is to investigate the assassination. Frieren doesn't go out of her way to do anything unless a grimoire is involved. She will fight back and kill if it comes to direct confrontation, but unless it's a demon she doesn't immediately go Terminator mode.