There are several reasons for bringing back the death penalty – in ascending order of priority;
1. It would reduce murders
2. It would improve police detection all round
3. It might make the police more culpable for their actions
4. It would make them more likely to catch the right guy.
5. It would make them less likely to frame the nearest guy.
….and THEATRE, the best reason of all - it would add greatly to public entertainment; the frantic last minute appeals to an unmoved Home Secretary then the silent early morning crowd in the rain outside the prison gate, waiting for the death notice to be posted - and afterwards a splurge of paperbacks from broke journalists/writers, '...did he or did he not do it?' (especially if he is a she..!)
...and it would give the elfs and fawns in Hampstead Garden Suburb another chance to hyperventilate while clutching at the drawing room curtains...