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?
"need for justice" makes it looks like it's a normal and even healthy thing.
Many people outside of the US are horrified at the thought families of murder victims going to watch the execution of the perpetrator.
Desire to see the perpetrator suffer is called revenge and is seen by many as a psychological problem in the victims that need therapy and healing.