Yes, but you seem to be missing the point of what the Sacrament of Reconciliation is. It’s not just “confession”…
I translate from the Spanish book “La Confirmacion” (RCIA) by Fr. Ricardo Fernandez:
The authority to forgive sins that the Church has is judicial: that is, the power conferred by Christ to the Apostles and their successors implies a true judicial act: there is a judge, there is someone being judged, and there is a guilt. A judgment takes place, a sentence is pronounced and a penalty is imposed.
This means that when the priest gives the forgiveness, he is not doing so as if he “declared that the sins are forgiven, but as a judicial act in which the sentence is pronounced by he himself as the judge” (Council of Trent cf. Dz 902)
The acts of the penitent: contrition, confession, and satisfaction.
Satisfaction is the final act of the sacramental sign, that in many places is called precisely penance. It is a sign of the compromise that the man takes to begin a new life
…being difficult that the dispositions be so perfect as suppressing all temporal penalty, the confessor imposes a penance that helps attenuating this penalty. It belongs to the substance of the dispositions (of the penitent) to accept the satisfaction imposed by the confessor in order to repay the divine justice; these works acquire supernatural value, because they are inserted within the effectiveness of the sacrament.