Leatherhead
Possibly a Idiot.
Really? Have you ever played in or even heard of a setting where an adventuring fighter is "completely justified and socially charged" with executing a defenseless bouncer, who just surrendered, in a bar, after a bar fight? The Hollywood mythos of the "wild west" is often invoked, but even in that kind of setting this would be murder (or a "wrongful killing," if you prefer). Even if the killer were not an adventuring fighter but a lawman or political/religious authority of some kind, there would still be a formal process for any rightful execution of the man, and cutting his throat where he kneels on the tavern floor is not such a process.
You just described Judges from the 2000AD comic. Or the Judge Dredd movie, which you might have heard of.