Why just kill him? I didn't see the point there..
What about beating him and mutilate his body again and again and then take him to recover and then again and again beat and mutilate until he is old enough to die for natural reasons?.. seems like a better plan to me.
Despite what I'm about to write, I'm generally against the Death Penalty.
The reason we don't do what you suggested is that it's animalistic and inefficient. Think to yourself: would you be better off and contribute more to society if you:
A) Spent all your money feeding, housing, and securely containing a man incapable of reform for the next ten to eighty years on the failing premise that reform is somehow possible for him who will likely never be released.
B) Actually used limited resources on people who can be helped, and who want to be helped.
Emotions can be overwhelming and cause irrational decisions, not unlike the white supremacist who acted on hatred. Do not let yourself be emotional like him. At least, focus your energy and attention on things that matter.
I suppose that's fair, considering the cost of the shelter in an existing prison is negligible, but that higher cost for the sentence is really only the legal defence costs for people who rely on the state for defence and choose to fight the sentence. The cost of the executions themselves are much cheaper, and I think on average the executions probably would be as well as long as more of them accept the sentence or pay for their own attorneys than the number who fight it on the state's expense.
The opposite could be true as well though, it could be vastly more expensive to try to execute them if everyone fights it on the state's expense.
Think about what you're saying... what good would this do now? You mutilate his body and let him recover then mutilate him again. What do we have now? One shooter with trauma who has been tortured and one heartless person (you) who tortured them.
Did that prevent any shootings in the future? Nope
Did it bring out the human in you? Nope
Did it help us economically save any money? Nope
Did it bring anyone back to life? Nope
Basically, in this scenario, you simply turn yourself into a criminal who probably deserves a similar punishment in that system that you're criticizing...