I don't understand how any argument in favor of it gets past this hurdle.
Its the end of the debate for any rational person, or anyone who could be trusted with such decisions really.
US arguably has the fairest system of determining innocence/guilt in the world, and yet it is still riddled with errors, and spectacularly open to bias, corruption, misinformation, inaccurate or non factual evidence, etc.
You can only get to the moral argument by narrowing it down to cases where someone admits guilt or there is hard proof, which IF there is a death penalty is what it should be reserved for, and even then from a moral/fair justice point of view I think its very difficult to make it make sense.
At the moment it isn't really much better than murdering innocent people, because statistically that is more than likely exactly what it is in some cases.