My argument is actually somewhat different from what you are describing. As the death penalty is now practiced in America, we take extra precautions with it, in virtue of its irreversibility. As a result, two advantages of the death penalty over life imprisonment are compromised. First, while most people think the state pays less by using the death penalty than it does in life imprisonment, the fact is that when litigation costs are factored in, execution is more expensive. Second, the deterrent effect is diminished, since not only does the criminal expect to get away with it (otherwise, he wouldn't commit the crime), but also, should someone actually be tried and convicted and sentence to death, death is hardly immanent, because the murderer can expect a long appeals process which is going to delay the execution for many years, assuming the execution occurs at all. This is probably the reason why crime statistics in states without the death penalty are no worse than in states with it. Having the death penalty just means that you might be sentenced to death, and then after 20 years or so, after your appeals run out, you may get executed, unless, of course, they decide not to execute you, which they might very well do.
So, it looks like the only way to make the death penalty do what we hope it will do is to "fast-track" it, eliminate the appeals, and make execution immanent for those convicted of capital crimes.
Of course, the irreversibility of the death penalty is an argument against its very existence. However, where we do practice the death penalty, we seem to concede an important point to its opponents, namely, that there should be a lot more appeals when we execute than when we imprison, because we can release exonerated prisoners, but not people we have executed. The result is that the two benefits of a death penalty seem to be either eliminated or greatly weakened.
So, if we have a death penalty that does what we want it to do, we have to accept the risk of executing innocent people and fast-track the death penalty. We have to not only risk executing innocent people, but we also have to increase that risk by curtailing the appeals process.
To do that, I think we have to abandon the idea that the execution of an innocent person is a more tragic failure of justice than the failure to punish a guilty person. I don't want to go there. But in order for the death penalty to have the advantages over life imprisonment that pro-death-penalty people think it has, it seems as if we have to go there.