There is a school of thought that the thing we should strive to minimize are first time offenders, this goal leads pretty naturally into a correct assessment that extreme punishment is a valid approach.

I take issue with that goal though, I think we should reduce the chance of future crimes from both criminals and people with no prior history in an effort to minimize the harm done to everyone - this is where I see a reason to fully forgive people. If someone could assure you (and be genuine in it, without strange conditions) that they would never commit another crime, then the only reason left to punish them is to demonstrate to society that the crime they committed is unacceptable - and that means you aren't punishing someone to teach them a lesson but to teach everyone else a lesson, if you could make it seem like they were punished but let them live a normal life that would work just as well (assuming they were actually hidden from view)