@wilddeath: I see your point. But the people here get invested and I personally also tend a bit more to share their POV. I also wouldn't like to see, if a normal criminal, that can be "caged" away is killed on the spot, when he is lying on the ground, but that guy here wasn't that harmless.
If somebody is holding a gun to the head of his own wife, because she truly wants to divorce this time and you as a police man want to save her, what would you do? The next moment that guy might aim at you or your partner. Surely it's a dangerous job, yet still you are allowed to protect yourself. And that wife. It is that guy, who is wrong. If he surrenders, all is fine, but while he doesn't, you wouldn't blame your colleague with the sniperifle for taking him out. It is allow and for good reasons. So, there are situation, when even your laws (and in this case our morals) allows to kill a person.
This case here and that one from my example aren't the same, but they share some common grounds. If that guy escapes or is set free for the same reasons that
@zeroxjac just wrote (zeroxjac took those words directly out of my mind.) his daughter and everyone around her is in danger again. This time that assassin knows MC's strength even better. There is good reason to assume he is capable of escaping. So his beloved one, himself and the next innocent bystanders are in a lifethreatening situation, that will most likely accrue. Also, what happens to highwaymen in this world? This "adventurer" in on the same or even higher level as them. It makes sence to leave him alive to interrogate him afterwards, but this guy is a psycho and supernaturally skilled.
Would you leave somebody alive, you can be rather sure not to return to you and your loved once? Sure. Even more, when you would get punished yourself. Outlawing death penalty in our world, when there could be still reasons somebody got sentenced innocently or might have a TRUE change of mind? Sure, why not. But would you also let somebody go, if you can be sure he will return to take revenge? And this is why the people here don't understand Daddy. He wants to protect his daughter with all of his might and knows he could have suffered defeat, yet he still clings to his morals, even though that seem to be the dark ages there and nobody would blame him. The people are still soft on him for calling him an idiot, instead of calling him an heartless asshole that values his own codex over the live of his daughter.