An interesting debate.
I am against CP, and as NewJudge has confirmed, it is not possible to be 'against' a concept on a sliding scale of merit - with the most deserving being executed, and the less deserving spared.
I am against it, not because of potential miscarriages of justice,that is a powerful argument, but rather that legalised murder has no place in a civilised society.
Capital punishment can never be anything other than revenge, and that does not belong in a civilised society either.
The notion of saving money by executing criminals is facile – if we are to incarcerate them for life, then preserving that life is a necessary part of the punishment.
Any sentient being reading the example set in the OP must feel the urge to destroy the perpetrators, possibly with as much pain and suffering as possible – that is human nature.
But sometimes human nature has to be subjugated for the good of society as a whole, where meeting violence with violence is a concept we are trying to eradicate, and controlled situations like the legal system are the best place to start.