Could it be said that punishment on a personal scale is communication? It seems to be the desire to control (as Maverick and others have posted), the desire for things to be done "the proper way" etc. Perhaps the whole spread of punishment (where one punishes the punisher or some bystander) is purely done out of a twisted sense of justice where the punisher feels pain and so inflicts it on others to make their own comparative state better.
Punishment should be, and sometimes is, a statement. It should say that the reason this person is being punished is because what they did is not acceptable and to redress the balance. Without punishment then there would be less cost to destructive behaviour, that's not good, but granted it is also often used to sooth the punisher's own feelings of inadequacy or vunerability.
I do not quite understand how destructive behaviour has less cost if there is no punishment.
I also am not a great fan of punishment for its own sake, although I do not think that satisfaction is an illegitimate goal for victims or their kinfolk, but I do think that sometimes believing that consequences and logical consequences will be enough to stop transgressive behaviour is insufficient.
It depends on the context and I do not think those things are used enough in teachable moments but there are some individuals, persistent offenders, who do not exhibit much in the way of teachability, I consider them exceptions rather than rule or norm but they exist none the less. Maybe they just do some sort of rational calculation and think that the penalty isnt great enough to dissuade them from a particular behaviour.
There is also the possibility that by choosing to avoid punative actions you appear weak or validating a particular course of action, people can wrongly believe there are no consequences to their actions because they have simply disregarded the natural and logical consequences and only pay attention to the formal sanctions. You could be schooling someone in that kind of expectation if you refuse to employ sanctions where it makes sense to do so.
I love the Punisher comics, TV shows, movies, I also love the archetype, in the comics Lucifer was kind of a Punisher character, although its only in the later comics that they really decided to make Frank Castle a sort of madman (like he was so much in love with punishment that he killed everyone he met because they were guilty per se, a bit like Judge Death and the other Judges of Deathworld who decided that life was punishable) earlier on in the comics he used to agonise the whole time about who he was punishing and avoiding innocents being injured etc. Its also make believe and apparently there is zero collateral damage.
When it comes to punishment I think you have to steer a course, dont facilitate a lot of sadists, dont spread sadistic social character, on the other hand dont encourage other sorts of sadism by appearing to support permissive norms or authorities.