Where state sanctioned killing is introduced violent crime and homicide typically rise afterwards. Potentially because society is saying its ok to kill someone if they really deserve it and your sure.
It is near impossible to be 100% certain of someone’s guilt. Even with confessions. They could be protecting someone or simply not of right mind. If the state makes a mistake it is permanent and is murder in my opinion.
Pricing has to take into account the legal costs a a printed with being as sure as possible etc. Even then there are cases of wrongful execution.
Three counter points: