No power in the hands of the state is more sobering than the power to end a human life. Only a handful of nations on Earth retain this power and the United States is the only western democracy among them.
Being an outlier on such an issue would be no problem so long as the United States derives some practical benefit from it, such as a demonstrable deterrent effect that has a downward impact on violent crime.
This is most certainly not the case. Capital punishment not only completely fails to deter people from violent acts but it is far from the most efficient means of dealing with the worst members of the human species.