Just because life in prisonment isn't a déterrant doesn't mean it's easy. Someone who kills another human being isn't thinking about the consequences because they're a psychopath anyway.
There's a reason we don't let victim's families judge trials, it's because we want justice not revenge.
If someone murdered a member of my family I would want to kill them of course, but I'm not in favour of the death penalty and it's a pretty weak reason for bringing it back.
Also can you stop avoiding the question about people who have been convicted of murder and served 20 years of their sentence before being found not guilty. Under your regime they'd have been put to death, surely the government committing premeditated murder of an innocent person in that case is just as bad as any other murderer?