Conquest #3 is a universal law.
Murder only refers to slaying by stealth or poison (so, I said stealth twice). Irresponsible homicide. Responsible homicide - from the front, declaring your intentions, using a physical weapons, generally giving them warning - is called vig.
To commit vig is to inherently risk your life. If you attempt to slay someone from the front, you believe they have done such a serious wrong that you would rather die than not attempt to offer it vengeance. If it's legal for you to slay them, a fortiori it is legal for them to slay you before you can manage it.
Who has to authority to deny such commitment? Nobody. Absolutely nobody. Not even the heavens will deny that level of dedication. Modern states profoundly offend the sacred when they dare try to abrogate it.
Further, open, public slaying means taking full reputational responsibility for the slaying. If you slay unjustly, all you manage is inviting your own retribution. Honourable slaying is nothing at all like murder.
When the State outlaws vig, it tells you that risking your life is meaningless. It tells you your reputation is worthless. "Betting your life is betting nothing and therefore accomplishes nothing, you disgusting peasant." It tells you dedication is bad, not good. It's bottomless evil, is what it is. Democracy is anti-democratic. It always levels down, never up, and does so unevenly.
When the peasants go along with it, they agree their lives are worthless, and thus make them worthless. They were told to treat themselves as meaningless and have obediently done exactly that.
The result is to protect the unjust. How many bureaucrats do something that's an unconscionable offence against dignity and honour? Err, all of them? Like, every single one? Every day? Legalize vig, and in no more than five business days this problem is gone. Yes, there is absolutely customer service so bad it deserves capital punishment, and if you're willing to risk them shooting back, then we have a guarantee that society is better off without that sinner.
What happens when you challenge one of them to a duel? Literally every asshole quits the next day. It's not like they don't know. The rest are scared straight instantly. They're astoundingly cruel but not so attached they're willing to pay with their life.
How do you get away with Rotherham rape epidemics if the dad can - and is expected to - shoot the fuck out of anyone who messes with his daughter? You can't, that's how. It happens maybe once or twice and then they're sidewalk stains. In a just society, sinners live in terror - if they live at all. As Saint Rittens demonstrated for us once again, the law-abiding can aim. Criminals cannot. It's no coincidence that "sin" literally means [to miss].
Bonus round: using [murder] for vig is straight Satanism. It's calling a rose a spade. It's a lie. Lies are bad, mmmkay.
Criminalizing vig protects murderers, and that's softballing it.