I think I reject the traditional concept of punishment (this is not to say that I'm opposed to measures that compensate victims though, because that isn't really punishment in the way I'm thinking of it, since the emphasis is on the victim's rights rather than simply harming the aggressor). I have trouble seeing how punishment is anything other than revenge, and I don't think that revenge and justice are the same thing by any stretch of the imagination.
The traditional view, however, is essentially that punishment is a moral remedy for a breach of morality. But I don't see how this can be the case when by definition punishment takes place after a crime has already been committed, i.e., it is ex-post-facto violence. It has no productive value whatsoever, it merely increases destruction to appease people's desire for revenge. It does not actually correct the wrong at all; if anything, it's "two wrongs make a right".
For example, putting someone to death in and of itself does nothing to remedy any crime that person may have committed. To be sure, it may ensure that the person doesn't commit any more crimes, since they aren't alive anymore to do so, but this does absolutely nothing to address the issue of why people commit crimes in the first place (and here I'm using the word crime in the narrowest libertarian sense of the term, i.e., a negative rights violation such as theft or assault or murder). All that's really gone on is that another person has been killed.
While there may be an extent to which the fear of punishment makes some people less likely to commit a crime, the fear of punishment in and of itself is obviously hardly enough to stop someone who's determined to commit such an act to begin with, since criminals by definition are people who engage in such acts anyway, regardless of the law or any possible punishments they may face. If anything, the ability of people to defend themselves, combined with social pressure or custom, deters crime far more than the mere fear of punishment could possibly do.
It also may sometimes be the case that punishment has the opposite effect of deterring crime. In particular, the current prison system essentially puts all of the criminals together (although of course a good deal of the people in there are there for victimless crimes) in a place where they can train as criminals and form criminal alliances. The vast majority of people who go to prison and make it out end up repeating the same behaviours or going on to engage in worse activities than before. Indeed, people who were otherwise peaceful citizens before can be made into criminals by their prison experience. There is a vicious cycle at play.
It is of course true that the fact that someone is in prison ensures that they can't commit crimes with regard to people in society, since they are isolated from society. Of course, the reductio ad absurdum this thinking leads to is locking everyone up in cells for their entire lives on the grounds that they might commit crimes in the future. In either case, the amount of actually serious criminals who are in lockdown for life in prison as compared to the amount of actually serious criminals who are running free is quite small, and it would be practically impossible to keep track of all of them. The fact that a handful of murderers are in prison hardly even begins to crack the problem.
The amount of people in society who are serious criminals (such as murderers) is likely fairly small to begin with. Outside of the criminally insane, there are very few people who would ever actually engage in an act as extreme as murder. It hardly seems to be the case that in the absence of draconian punitive laws everyone would go around murdering each other; a ridiculous argument from doomsday if I've ever heard one. The person who says that in the absence of such laws or the punishments that go along with breaking them they would have no problem engaging in theft and murder either has a very low moral barometer or they are simply deluding themselves.