Either you consider human life a fundamental value, or you do not. There are no final answers in this mysterious, apparently indifferent universe, but there is a lot of empirical data. Over and over, cultures that place a high value on human life lead to the societies where the most people prefer to live.
Another issue is that an old religious superstition survives even among atheists/agnostics, because it is disguised as a philosophical concept. This superstition is called "free will". Some people are born with problematic brains, others are raised in environments where they never have the chance to develop a healthy mind. Does society have to protect itself from these people? Absolutely. Do we want to live in a society that decides to kill them because it is more economically effective? I don't.
Yet another issue is that of certainty. It is never possible to be 100% certain that someone is guilty. Even if they confess, even if there is video evidence. There is always a tiny probability that there is something fundamental that we are missing. A culture that place a very high value on human life will not be willing to take this chance.
Consider also that, in the EU, not only is there no death penalty but not even life sentences. Typically, the harshest sentence you can get is 20-something years, no matter how terrible your crime. And yet, there is less violent crime in the EU than in the US. EU countries spend much less resources in keeping people incarcerated than the US. Why do you think that is?
How can you know that what you're saying is not a superstition itself?
Which isn't to say you're wrong, but I think it's pretty uncharitable to say there aren't any "coherent" arguments in favor of free will. You did say you haven't "seen" any arguments, which I suppose is not the same as a claim that are none, but a cursory glance at that article should be illuminating for you. People have been thinking about this for a very long time, and no consensus seems to have emerged. :-)
You might also be interested in http://plato.stanford.edu/entries/materialism-eliminative, which seems to fit what little you've said about your current thinking.
I'm not saying that this is the argument to use for abolishing the death penalty, but it's definitely not one for keeping it as it currently stands.
I think the decision between life and death shouldn't be made based on cost.
In many cases, guilt is not certain, only proved beyond a reasonable doubt. Lifetime imprisonment can be reversed if a mistake is realized, but death can't.
Even given a hypothetical case where the evidence is so damning and guilt is fairly concrete, the execution of another human should be a punishment reserved for when we have no other option.