Perhaps I misunderstood your intent in the first post. We’re you suggesting that if the government’s laws specifiy death as a penalty then that is legit?
Paul was saying one of the reasons God establishes governments was to punish evildoers and that the death penalty is one of the ways God metes this punishment out.
What part of “sword” in Paul’s statements did you not understand...did you think it meant Governments tickling murderers with chicken feathers at the same time trying to shame them like a neurotic overbearing mother?