Well, it isn't that punitive measures serve no purpose. They do. But that purpose doesn't decrease the chances of a given crime occurring by other people, nor does it prevent the same people repeating a crime. To the contrary, the way most prisons work, chances are that anyone going on comes out with less options, and more knowledge of crime, so even if they don't repeat the same offenses, they're put in position to do others out of necessity.

But it does seem to make people feel better when someone else gets punished for doing something wrong. Which, in theory, is going to reduce vigilantism and mob justice. In practice? I dunno, I haven't seen enough data to form an opinion about that specific matter.

Generally, the reason it shouldn't be the main goal of a justice system is lack of efficacy. It just doesn't do what people want it to do. So, what's the point of that?

If your goal is to reduce crime, and reduce recidivism, rehabilitation has shown to do a better job. Prisons should be the last resort for non violent crimes, not the first. Even then if prisons hope to do more than isolate repeat offenders, they would need to have more intensive measures to help people change.