Death penalty is an ineffective deterrent mostly because people tend to commit the crimes it’s used as a punishment for while not thinking, or caring, about the consequences at all.

Now, forget cutting off the internet, if you’d get the death penalty for getting caught pirating music, it would prove to be a very effective deterrent at stopping it. I guarantee, zero piracy after a few years.
A lot smaller population left to buy the legal media too, though, but hey, no pesky pirates!