> What those consequences be if the society does not punish people for that?
Given the state of most prisons in the west (Especially in the US), we are often sending people to effectively rot and even if they get out they might as well be dead they're so stunted.
Indeed, you can't bring dead people back to life. Judicial systems should not be based off of the emotions of people affected by crimes - it's not a nice thing to say but it just empirically doesn't work.
> For this crime any punishment is exerted only as a message to other people: don’t kill people or else those bad things will happen to you.
Not only is deterrent-policy usually very expensive both directly and in the aforementioned tendency to shit out people who go straight back into crime, I'm not aware of any studies that manage to disprove their null.
https://deathpenaltyinfo.org/policy-issues/deterrence
In the extreme "capital punishment means those without capital get the punishment.".