This one is always a hard topic when it comes up. Mainly because the issues surrounding why such a punishment would be considered can be so very complex. It would take a very long time for me to explain why I think it's necessary. So I'll try to keep it simple.
As a society I believe that we need to be accountable for our actions. If we willfully murder someone (this is where it gets tricky since war and self-defense are different) then we need to be prepared to accept the consequences of choosing to kill someone else.
So yes I think it should exist. However, I also think it's something that should be carefully considered and rarely used. Anyway, what are your thoughts?