Yes, I actually recognize that the government has a selection of abilities which are used for the well-being of its citizens and that murder is different than the other cases you posted due to the presence of the killer's intent, the lack of consent and if the target is defined as a victim with rights that need to be protected. State-sanctioned though it may be, capital punishment still seems an awful lot like murder and I'm not entirely sure what we hope the government will achieve with it. It doesn't seem like much of a corrective measure (sure, the condemned won't be committing any crimes afterward, be he or she won't be doing much else afterward either, and you could probably also cut down on that particular individual's crimes with incarceration, barring the corruption and thuggery present in the penal system). Jury is still out as to how effective it is as a deterrent (the states without it tend to be on the lower end of the murder rate scales, but no one is going to point to it as the sole deterrent when there's dozens of other social factors involved like poverty). I guess it's a retributive measure, but I'm not sure if I'm really all that comfortable with the "eye for an eye" philosophy. Imprisonment in theory can be used as a corrective and rehabilitative measure, but America's love with the idea that prison is a place where bad people go to get brutally spanked by daddy government leads to horrific abuses by such lovely individuals like Maricopa County Sheriff Joe Arpaio (who has been re-elected four times despite being a rancid stain on the trousers of justice) and a brutal culture wherein prisoners whose crimes may not have been all that brutal to begin with are thrown into a balkanized battleground and if they get out there's a good chance that they'll not only be changed by the environment but also be essentially unemployable and thus at a high risk for recidivism. And like the death penalty, it all gets held up as a reason not to commit crimes. But if the only reason someone is avoiding committing a crime is because he or she fears the punishment (or rather, fears getting caught rather than the specific nature of the punishment), that's not a very reassuring situation.