...and vengeance too.
However, the right of JUSTICE belongs to the USA and one part of justice is punishment.
Those who do not believe in the punishment of the guilty, do not believe in justice.
Add: Retribution.
Punishment is for those who commit a wrong or crime, to encourage rehabilitation and also to grant socity it's due vis a vis the wrongdoer or criminal.
Retribution is meant to send a powerful message to others that strong medicine comes to those who would consider a monstrous act.
IMO, Justice for an act commited is not enough to deter fanatics. Only the certain knowledge that fanatical acts will bring retribution to the fanatics themselves, their organizations, their extended families, and their entire people will possibly dissuade them. This requires more than punnishment, but knowledge that retribution will be swift and terrible.