Retribution Theory
Why do we want systematized vengeance? Just because we want to take revenge, doesn't mean that we should.
No, I think now we get to the meat of your problem; the dichotomy of values and wants.
In reality where can you find the "should" if not from wants? Ultimately how do you justify it?
The only way I can see is if you set one up arbitrarily(categorical imperative, greatest good) which itself is merely a want.
In effect you are for the most part presuming that vangeance is only an extrinsic good. I and many, many people however see it as intrinsic. If someone wrongs us, we wish to revenge.
I'm not sure of why this is. In fact most people are not. But then again most people do not know why they feel a certain way about a great many things. People in the Middle Ages did not know why they liked meats, why they thought murder is wrong, why they wished to keep on living. But that didn't stop them from pursuing their values, pursuing their wants. Wanting is in itself a justification, wanting is the end that a "should" merely proposes to help you attain. Wanting is an ultimate jutsification, though not a full explanation.
I should also note the case against the death penalty is also based ultimately on emotion. The emotional appeal that we not be "barbaric"(which is merely a label given to something seen as unpleasant/undesired) or that we make it so no innocent person get punished, no matter the circumstances(a bit more complex an argument then the former of course based on less value for punishing the guilty and far more for sparring the innocent). Though I don't see how the latter applies to some very clear cut cases.
I CAN go further though and explain why I believe people have come to want the death penalty(a more ultimate explanation), basically it has to do with evolution.
During evolution organisms try to exploit eachother. Members of our species were no exception. Hence often times an animal had to resort to counter-agressive strategies: fighting back. This made them less likely to be exploited. But with more complex animals its different, you can fail once and try again, especially with humans. This is where mere momentary counter-agression is not enough. Merely stopping a guy from killing you during it is worthless if he simply gets to try again and again. This is where a more long-term retaliation, vengeance comes in. An organism is far less likely to attack an organism that will take vengeance, attack back, then it is that will passively either accept the assault, or defend itself till you stop.
Tell me what would you think of as more prudent to attack if you were a thief: someone who will stop you IF they catch you, or someone that will stop you and hurt you if they catch you or find out you stole?
Given a choice a prudent thief will always pick the former.
This applies to nature as well. Animals who merely defended were more likely to be exploited then animals that took vengeance.
I believe then that as animals became more intelligent, learned how to calculate odds and take advantage of others more easily, this sense of vengeance was more essential for societies where one person will quickly realize whether you will take vengeance or merely defend yourself at the moment. Hence vengeance evolved as a preventive measurement, as an extrinsic good.
But genes often times work indirectly, and extrinsic ends over times can only be consistently practiced if they are made into extrinsic values. Our enjoying foods is essential for our survival but how often would you eat if you did not enjoy the act itself? If it was neutral or considered a sort of labor? Less often then if you enjoyed the act. So the act of eating was made an intrinsic value, because it was so essential nature simply turned it on for good. Animal brains at times are also not developed enough to consider long-term goals and extrinsic values, so nature has to often time resort to emotion, making extrinsic values for the genotype intrisnic for the animal to get the animal to go for it at all.
And I believe in our complex, calculating societies vengeance was the most important of values. If people willing to exploit others knew you were a push-over, they'd take you for all you were worth. And they would quickly find out if you were one via gossip. Hence like the thief scenerio, if you would merely defend, they'd be more likely to attack you then if you didn't just stop at defense and took vengeance(especially if you were the type that took vengeance even if it hurt you as well).
Hence I believe this value, extrinsic to the genotype, by being so essential, became an instrinsic value for the phenotype, a basic emotion or desire. And there is no other basis of moral or behavioral justification then our basic emotions.
Now this theory isn't a science. I wouldn't go so far as to say it is a scientific theory. It is mere conjecture, but I would say conjecture that makes sense, explains a lot about mine and apparently mankind's emotional mechanisms, and has *some* basis in scientific literature. Read Steven Pinker's the Blank Slate where he explained how our sense of retaliation evolved in order to help an organism avoid being exploited.
I'd also like to point out that the justification(in the ethical sense) for the death penalty is still raw emotion. Just as the argument against the death penalty comes down to raw emotion(or lack thereof). And my evolutionary conjecture was offered as mere explanation for why this is so. To make this point more explicit, I like playing games because its fun, not because it helped my ancestors survived. Knowing how playing games helped my ancestors survive would merely explain why I felt this way, if the game got boring though I'd stop playing evolutionary precedence or not.
And this is where the government comes in, as a force that allows us to attain our values in a more organized and efficient manner.
The government protects our most core extrinsic and instrinsic values: education, knowledge, progress, freedom, life, peace and prosperity.
And this goes the same for justice, vengeance. The government in demanding we cannot be allowed to pursue such a strong and universal value ourselves has to give us something in return if it is to retain legitimacy to deprive us of our personal vendettas. What the government gives in this respect is social justice, the fact that it will take vengeance for us, since it demands we do not do so for ourselves.
This has the advantages of keeping order, allowing the weaker party to attain justice, and enforcing justice more efficiently(by making sure less innocent people are harmed; which benefits both parties, etc.).
This is why for example we go after Holocaust criminals, even though it is unlikely to benefit our society in any other way, to bring back the victims, or even to prevent another genocide. Even IF they could prove that punishing such or any authors of genocide is unlikely to prevent genocide again, I and many others(I day say even those against the death penalty) would still probably want such people punished. Purely out of our sense of retribution.
This is thus why we want systematized vengeance, answered in the area of justification and (to a limited extent) in the sense of explanation.
I love throwing out wild statements and then backing them up 
But, let's look at this.
