I think no other justification is needed to end the death penalty than “it’s inhuman and barbaric”. Even discussing other factors arguments and considerations dilutes the core point that’s it’s straight up wrong unethical and inhuman to murder others in the name of the law. Paul Graham has a valid point, but if you say “it’s wrong cause it’s inaccurate”, implies it’s right if it’s accurate. And it’s not... the death…
Criminals sentenced to death are supposed to be a danger to society so great that the only solution is to eliminate them. So, typical trolley problem: is it better to kill a criminal or let him go, potentially resulting in the death or several more innocent victims. Prison for life is another option, but is permanently restraining someone and endangering guards and other inmates a good alternative?
So yes, other justifications are needed. And the article gives one.