It won't teach the perpetrator not to commit the same crime again. Malice only breeds malice.
If it is deterrence, you're too late as the act has already been done; you may argue that it might stop others from committing it, but since this was a deeply irrational crime reasonable consequences didn't factor into it.
Making the victim feel better? Seeing their attacker hurt may seem cathartic on a visceral level but it won't undo the damage.
Making you feel better? That wouldn't be justice, that'd be sadism.
Torturing criminals to "make them feel the same pain" is a visceral response that brings brief gratification, but it's not a solution to anything.
So the judgment on whatever should happen in case where guilt is really not in doubt must be reserved for omniscient infallible divine beings, as we the people simply are not capable of implementing a process that's able to determine when guilt is not in doubt, as all practical experience shows that we've tried and failed and failed and failed to do so.