It's a good thing the extra rigor applied to death penalty usage in the US causes it to be more expensive than life imprisonment. Giving the state a fiscal incentive to execute would be heinous.
Weighing economic costs against a human's right to live looks like a very strong indicator for a barbaric society to me. Although I'm aware that this is done (implicitly) in probably all societies to some degree.
Locking someone away wrongly for a year or twenty years is also permanent in that they can’t get that life/time back, even if they’re still alive when found not guilty. It’s just permanent and slightly smaller, but still a horrific theft IMO.