Why not? It's fascinating the philosophical hoops we jump through to justify what is a disgusting, barbaric act however you actually do it. Anyone who supports the death penalty should be required by law to watch it carried out.
I say, let's put it to a majority vote. Everyone who votes in favor of killing is put into the pool of executioners (just like jury duty). It's one thing to be abstractly in favor of killing as a punishment. It's another to look down the sights at a fellow being and pull the trigger.