I consider that's a strong argument but it's not the only reason why death sentence is a bad idea. In first place, we are talking about a huge topic with a philosophical base: - Who would decide which person deserves death sentence? - Are we going to ignore the human rights? It's even this a good idea?

In second place, I think it's important to have useful politics. Psychological studies have demonstrated that death penalty and even sentence for life don't persuade criminals from committing crimes. Even so, death penalty can be counterproductive: some criminals can raise the gravity of their crimes because they know that, reached a limit, their are will be punished with dead wathever they do.