So you think that prisoners cost you too much money and thus want to execute them?
No. I've never made that argument. I think Dio might have, but I'm more familiar with the facts. It costs more to execute a prisoner than to keep them for life in prison, because of the cost of the appeals process. Efficiency and cost are not reasons to kill anyone.
For me, the biggest reason is, we need to be able to say some crimes cost a person their life. We need to be able to say that for deterrent reasons, and for the sake of justice herself. Civilization requires a social contract, and things like murder are violations of that contract that must entail the most dire of consequences. Would-be murders need to understand, that when they murder someone, their act is an act against all society, and their life is thus forfeit.
You should not presume that every time someone acquainted with an unusually heinous crime responds that the criminal should be executed, that the person is suffering some revenge thing. Retributive justice is not based on revenge. Theories of justice distinguish between retribution and retaliation specifically because since the time of Jesus Christ, most thoughtful people understand revenge is not justice. It's an emotional knee-jerk reaction.
Just to be clear here, the ancient mosaic code that most of Western civilization is based upon, is not based on revenge or retaliation. "An eye for an eye, a tooth for a tooth" was never meant to be revenge. Rather, it was seen as the limits of retribution, using the consequences of an act as the guide for a judge in a court of law, to measure out justice and limit that retribution. I'm not aware of any ancient Jewish judges ordering someone's eye plucked out. That's a modern caricature intended to mislead those unaware of what Moses actually wrote. What he wrote was a guide for judges in a court of law, limiting the sentences of those who had committed crimes, based upon the theory of retribution.
What most people today think of when they hear "an eye for an eye" is what's known as the theory of retaliation or revenge. That is NOT what Moses was all about. When he set up the Jewish courts, he also set up the sanctuary cities where the accused were safe from revenge. He was in fact setting up the basis for setting personal, emotional vendettas aside and making a way for courts of law.
So in general, it is wise to precise this difference between retribution and retaliation. Retaliation/revenge never leads to justice.
"Courage is not just a virtue, but the form of every virtue at the testing point." C. S. Lewis