Of course they should be punished, but punishment should always be a part of rehabilitation. That doesn't mean coddling or protecting, as such, but means making sure they get better and don't do it again.
Look at the high amount of recidivism in convicted child rapists. This is not entirely a matter of revenge, it is removing a horrific and dangerous member from society and ensuring that they NEVER commit such a heinous act again. Death has a 0% rate of recidivism.
And also helps prevent others from committing the crime too. Less child rapes is what we want, right? Well studying rapists is by far the best way to do that, understanding why it happens, as all human actions have motivations and are always within a context, is by far the best way to make sure those motivations don't grow to that scale and those contexts don't occur as often. Killing them solves absolutely fuck all, the child was still raped, and there's no getting away from that, and we can't learn anything about the rapist because, shit, they're dead.
What? Sociologists and Psychologists exist pretty much entirely to study phenomena like this, and have done a pretty damn good job of it. We
do know why people do this, and it has not vindicated them in the slightest. What kind of "studying" do you think needs to be done? We already understand that they do this out of sexual deviancy, lust for power, or because they themselves were molested as well as a variety of other causes that vary by society and culture; what else do we need to know? "Killing solves absolutely fuck all!"? Really? Again, it ensures that they NEVER rape another child. How is that "fuck all"?
However hard you want to bang the drum of justice, demanding that revenge should be taken out on those that commit horrible crimes, you will do nothing to serve the cause of helping and preventing child rape.
I've said it multiple times, but I will reiterate: Killing these individuals ensures the safety of potential future victims at the hands of someone who has proven that they have no regard for the human rights of others.
I would also like to air this point, though it is far from conclusive and more speculative. How far do we say "This child is now beyond hope, their life has been taken, and they will never have a good life," when we put someone to death for that crime? Are we saying the child is beyond hope and thus the rapist should die to make up for it? While I cannot imagine anything more terrible than that act, and have little experience with those that have been affected by it, I would never, ever suggest that they were totally beyond repair. I don't think many would like to say that, or believe it, either.
I have had the unfortunate experience of witnessing the effects first-hand, and I can assure you that you are underestimating the trauma caused by such an event. As much promise as an individual child might have had, as much potential as might have been contained in them, they will almost never be able to achieve the quality of life they would have been able to had the event never occurred. I have seen children with so much promise, so much life in them have their entire existences destroyed simply because some sub-human monster viewed them as nothing more than a sex object and acted upon their lust. Of course we don't want to admit it, we want to believe and do the absolute best we can to ensure that the victim at hand has the best quality of life possible, but the fact of the matter is that children who were raped are exponentially more likely to develop mental problems and commit suicide due to the trauma of their abuse. The victim will
never again be the person they were before the event, which equates the rape of a child to murder in my opinion. This is different from when an adult is raped, because although the act is still extremely heinous the victim in question has a fully developed personality and has already come to terms with themselves and the world. A child does not have these advantages, increasing the damage done horrifically.
Rapists of course shouldn't be coddled or protected, to say that is my argument, and that it is either that or death, is a fallacious distraction from the argument at hand. We don't want to admit they are human, we want to say they are monsters. But humans can be monsters, and I think whether we like it or not, in some possibilities I think the capability for such 'inhuman' acts lies within all of us.
Death is not the only option, but it is the safest in my opinion. One who has demonstrated that they are willing to brutally violate the human rights of a child should never be released back into society; whether through life in prison (which would allow your "studying" to occur, whatever that might be) or death (which would indefinitely prevent them from committing the same crime again) the safety of the public must be ensured.
Also, of course the capacity for 'inhuman' acts lies within all of us. I could post this message, walk down my street and kill the first person I meet. So could you. But neither of us will, because we have moral and ethical values that ensure we don't. Why should pedophiles be held to a different standard?