I think it should be both. Punishment can be a good deterrent, and it’s really not possible to measure how much of an effect the deterrence has. You don’t have statistics on people who would have committed a crime if there weren’t harsh punishments.

I know it’s off topic but what has been proven to work best is to prevent crime by improving the lives of would-be criminals before they get to that situation. It’s cheaper and just better in every way.