@gollum,
The plaintiff gets the punitive damages because the plaintiff brought the lawsuit. If the plaintiff had to give all of the punitive damages to the state, there would be no incentive to seek them in the first place. Yet the judicial system recognizes that punitive damages serve a socially useful purpose, in that they express society's strong disapproval of certain actions that do not, however, merit criminal sanctions. So either the plaintiff gets the punitive damages as a reward for pursuing what is, in effect, a social purpose, or else the state gets involved in every case where punitives might be available, which would be enormously costly.
That being said, I know that there are some jurisdictions where a portion of punitive damages are awarded to the state. And there are, of course, many places in the world where punitives are not available at all.