The point is people don't die at the hands of the state, unless there's a judicially sanctioned lynch mob, but at the hands of a professional killer paid out of public money to do their dirty work. Add the physical and emotional apparatus surrounding judicial killing and it becomes a grim business indeed.
I agree that for unrepentant serial killers, child murderers, psychopaths like Shipman the reasons to allow them to remain live are difficult to support, especially bearing in mind the cost to the public purse and the feelings of the victim's family, but is paying a hired killer an appropriate way of settling the issue? Albert Pierrepoint became convinced hanging was ineffective as a deterrent, and he was the last man to look into the eyes of hundreds of condemned prisoners.
I would suggest a doctor to administer a lethal injection as in a case of euthanasia.