You say that one reason why forgiving is good is because it could get the attention of the one who acted wrongly. Yet, what if the forgiveness never does get the other’s attention? It then seems to me that you have wasted your time in forgiving.
Forgiving when properly understood and willingly chosen to practice is never a waste of time. This is the case because, as a moral virtue, forgiveness is good in and of itself. In other words, when a person finds the strength and courage to be respectful, kind, generous, and even loving toward other people, even when they behave badly, this is a heroic act. Of course, we have to make a distinction here between forgiving and reconciling. Automatic reconciliation which could be dangerous for the forgiver is not wise. To unconditionally forgive, offering goodness while “watching one’s back,” is good because all moral virtues are good.
For additional information, see: Why Forgive?