I keep returning to that article you posted and commented favourably on post correction. See, at some point in that attack, the father stopped beating up "the person sexually molesting his daughter" and started beating up "the person who had been sexually molesting his daughter" - unless, I suppose, the deceased was the most single minded molester in history. And even if we allow "self-defence" to include protecting one's family, which I have little argument with, once that point was reached what you have there is revenge. He should be in jail.
It seems that you are taking a very simplistic, and perhaps even theoretical, perspective on this. A criminal does not suddenly jolt into a rational mindset and stop his actions upon being inflicted with a first, 'self-defense' blow to the head (or in this case, father-defending-daughter defense blow).
In the case of that father, what likely happened is that he witnessed this man molesting his daughter, so he punched him in the head. At that point, the molester likely was acting in "his own" self-defense, and readied his own fist to return a punch. To avoid such a situation, the father probably continued to beat up the man, which ultimately led to his death.
There is simply no way to call the police department for a 'lawful' arrest in that short period of time. You are correct, this would be the "ideal" in a theoretical sense, but in practicality, this is not feasible.
The point is, "self defence" isn't entirely what anyone is talking about. If I jump out of an alley at you and point a gun, and you shoot me dead, I simply don't see how that is self-defence. I haven't done anything at that stage beyond frighten you. Burglary doesn't carry the death penalty, unless the home-owner has a gun and is willing to use it. There's no justice at all there, just civilians taking life and death matters into their own hands with no oversight or training.
Everything you are saying is theoretically correct, if we were observers of an incident, and we know the intentions/motivations of all parties involved. But if someone is pointing a gun at my head, there is no time to have this sort of analytical discussion on his potential intentions. I have to fear the worst for my safety, and whomever I am with, because if I don't, a bullet will instantly kill me on the spot.
The way I see it, no one in their right mind would attempt to point a firearm of any kind at my head in public, unless they had deadly intentions. It is not a toy, it is a lethal weapon, and should be used responsibly.
That is why some of these pranksters on YouTube are really asking for something tragic with some of their 'extreme' scare pranks. If they had some sensibility, they would exercise more caution.