It's not about making the murderer suffer either, it's about preventing future crimes. When you have cancer, you don't kill cancer cells because you want them to suffer. You kill them to prevent them from killing you.
Turns out the only thing harsher penalties do (beyond a certain threshold) is make it more likely for crimes to escalate because there's no point restraining yourself (if it means leaving witnesses) if you're already going away for life / going to be murdered by the state anyway.
As a matter of fact, the best way to prevent crimes is actually preventing crimes. Figure out why people commit crimes, then try to fix that. E.g. if you stop treating addicts as criminals you can solve their underlying psychological/social problems and they don't end up robbing people to pay for drugs.
What, exactly, is the point of punishment?
Are you trying to prevent future crimes? Great, we're actually talking about crime prevention and severity of punishment is a red herring (because we actually need to consider punishment as merely one option among many).
Are you trying to satisfy victims? Okay, but now you're saying the punishment basically serves as a synthesised substitute for mob justice -- so why pretend there's anything humane about it at all?
Are you trying to deter other would-be criminals from doing the same? Great, we can actually measure the effectiveness of that empirically (spoiler: it's not great) and adjust punishments accordingly.
Or we can just build more prisons and put more people in jail (or murder them if we really don't like them) because that has worked out so well in the US.