Simple, they want the public to believe that if they follow in the killers footsteps, they will be caught and go through hell in order to dissuade other people who might do the same. There are obviously a lot of people who applaud his actions, so to try to prevent them from getting the idea that they can do this too, they make a show of force to make them think twice.

In the end it doesn’t matter if Luigi did it or not. As long as people are scared of the pinishment, they will hesitate to imitate.

Not true justice, but they never really cared about that to begin with.