This is usually shonen logic. It's quite rare to find it in another genre.

Yeah, its a running trope in shonens.
Shonen have the habit of trying to teach kids valuable lessons, "dont give up on your dreams" for exemple.
As for this trope in particular, i think the lesson is something along thoses lines: Forgiveness will pay far more in the long run than holding a grudge will.
Or something like that.