Theories of the atonement are usually categorized as “objectivist” or “subjectivist.” Objective theories claim that the death of Jesus paid for sin and therefore reconciled God and man. Subjective theories claim that the real action of the atonement isn’t in the event of the cross itself, but in the effect that the message of the cross has on its hearers.
Isaiah 53 doesn’t provide a theory so much as a drama and narrative of atonement, but that narrative cuts across, or synthesizes, objective and subjective. On the one hand, the Servant suffers for our iniquities and bears our infirmities and the chastisement that brought peace falls on Him. Objectivism for sure. Yet, on the other hand, the drama of the story is not only about the Servant but about the many who first recoil from the mangled Servant and then finally recognize Him as their sin-bearer. The Servant makes reparation by His obedient suffering, but this changes the many when they perceive that he is not, as they thought, God’s enemy but God’s Servant. Without that “subjective” response (which includes the incorporation of the many into the mission of the Servant), the Servant’s work is not complete. Let’s say this: The crucifixion narratives must be completed by the heart-piercing repentance of Acts 2; the cross must be followed by people who look on the one they have pierced and mourn.
The bridge between the suffering and the repentance of the crucifiers is the exaltation of the Servant. When they see the Servant vindicated, they realize that they had misjudged His standing before God. In New Testament terms, it is the resurrection that vindicates the Son and the message of His resurrection and exaltation that produces the effect in those who crucified.