Before talking about the essential role of the death penalty, you have to think about the meaning, and the purpose, of any kind of punishment. If you consider that the purpose is to prevent the guilty from being nasty again, you can be seduced by an argumentation in favour of the suppression of capital punishment.
But you have to think about another aspect of the problem: a punishment is also useful to impress people, to make them fear the law. In fact, let’s take the example of a young misfit, which has grown in a violent atmosphere, influenced by older delinquents, etc. He lives in the streets; he’s got no aim but to survive. This is the kind of person who could possibly kill someone for money, or even for fun. Why would he fear prison? Life would be easier for him there. In addition, in many cases, when you behave normally, you can benefit from penalty reductions. This young misfit needs to be impressed; he needs to know that the law is a frontier. When you cross it, you can lose your life. That is why capital punishment helps keep a distance between robbery and murder. If you abolish it, you suppress the difference between these two types of crime, which are completely different.
But there is also a limit to define: even if the death penalty is unavoidable, it would be a crime to apply it to inadequate cases. If there is no premeditation or past facts which can justify such a punishment, it is far too strict to apply the death penalty. That is why the lawmakers have to establish precisely the context in which capital punishment car being pronounced. That is the price to pay to limit violence without using excessive violence.