Oh you are just being squeamish. If reducing the murder rate was an objective, the US would ban guns, period. The excess murder rate in the US is entirely due to guns. Take out the gun deaths and the US murder rate drops to the same as the UK.
The real function of the death penalty is the same as reality TV: it gives the people whose lives are otherwise rather boring something to feel good about. So from a functional perspective it really doesn’t matter if the person is innocent or guilty, thats not the point.
Some people just don’t feel comfortable unless they are being governed by a person who enjoys an execution. So they elected George W. Bush (sort of) and were all surprised when he went and murdered half a million people in his war against Saddam.
The death penalty is a sexual fetish for sickos.