On the other hand, it can be equally traumatizing for the victim's family to see the perpetrator get off with a slap on the wrist.

We don't have to go into the extremes either way.

Also, the desire for punishment is is not about seeing the perpetrator suffer, but about paying for the damage they've done. If someone bumps your car, would you describe the desire for the guilty party to pay for the damages to be a mental illness?