Historically that's also why we moved away from execution methods like hangings.
We kind of distilled down a way to remove people from the equation as much as possible to both I guess spread responsibility (making a large group of people have a hand in the execution to the point where no one person is singularly responsible), but also we seem to have gone out of our way to automate a lot of what goes into an execution to sterilize it of guilt as much as possible. This is at least part of why I don't believe in it.
I feel that execution is vengeance based. It's not about making the person pay for their crimes (because very often prison is a worse experience than death).
Justice is about repaying a debt to society and being rehabilitated. If rehabilitation is off the table then the next best thing is to incarcerate a person so they can't be a threat to themselves or others.
The US is terrible at both somehow and I don't like or believe in our justice system but for a bar that was already in the basement we sure did find an elevator headed down didn't we.