To continue my analogy, then, if people in the future have faith that I cut off my finger, can they be absolved of parking tickets?
The analogy is not quite right because it ignores the ancient legal concept of vicarious expiation, in which the guilt of a crime can be transferred onto a third party. This is the basis of the sacrificial cult, in which a person could atone for legal infractions through the offering of scapegoats and other animals. The logic of sacrifice is not to please an angry god but to offer an innocent substitute that can legally bear the guilt that one would otherwise pay the penalty for (i.e. through lex talionis).
This legal provision was then utilized during the Exile as an ground for hope for the restoration of Judah. The Deuteronomistic view of history shared by the exilic prophets explained the destruction of Jerusalem and the humiliation of the Exile as punishment for crimes committed by the nation and the sufferings of the exile community were construed as expiatory for the nation as a whole. Deutero-Isaiah symbolized their sufferings through the figure of the Suffering Servant, who is described as justifying the rest of the nation by "taking their faults on himself" (Isaiah 53:11), thereby giving reason for expecting a full restoration of Israel (ch. 54). But the hopes were not realized, and instead Jerusalem came to be punished by an even worse persecution during the time of Antiochus IV Epiphanes. The author of Daniel explained the apparent failure of eschatological hopes; the seventy years of Jeremiah was in reality supposed to be "seventy weeks of years" (i.e. 490 years) which were decreed for "putting an end to transgression, for placing the seals on sin, for expiating crime" (Daniel 9:24). This provided the perfect means for offering solace for the Maccabean martyrs who were innocent of any crime but who were put to death for refusing to turn away from the Law. Their deaths were not in vain, but allowed the nation as a whole to repay its legal debt for sinning before the Exile. Such martyrs are "purified and made white" (11:35) through their sufferings and they "make the many righteous" (12:3), a phrase that is a clear allusion to Isaiah 53:11. Thus, such martyrs were viewed collectively as the Suffering Servant of Deutero-Isaiah, and the promised blessings were faciliated by their sufferings. The martyrs themselves would also share in the blessings, for Daniel has added a belief in resurrection to the eschatological hope (Daniel 12:2-3). That this view of the Maccabean martyrs furnished the substance of the NT views of Jesus' death as expiation can be seen from the following passage from 4 Maccabees:
"These them having consecrated themselves for the sake of God, are now honored not only with this distinction but also by the fact that through them our enemies did not prevail against our nation, since they became as it were a ransom for the sin of our nation. Through the blood of these righteous ones and through the propitiation of their death the divine providence rescued Israel, which had been shamefully treated...Those men who surrendered their bodies to suffering for piety's sake were in return not only admired by mankind but were also deemed worthy of the divine portion. And it was because of them that our nation enjoyed peace, they revived the observance of the Law in their land and repulsed their enemies' rage. And the tyrant Antiochus was punished on earth and continues to suffer punishment in death" (4 Maccabees 17:20-22, 18:3-5).
By the first century AD, eschatological hopes of a restored Israel were still not realized and hence the popularity of expectations of a messianic deliverer who would bring about these blessings. While different groups has different ideas of what the ideal messiah would be (i.e. as a militaristic Joshua figure, as a legal Moses figure, as a priestly Levi figure, etc.), some early Christians viewed Jesus as an expiatory messiah, who would bring about the blessings through giving his life as an expiation for sins, just as the martyrs did in Daniel and 4 Maccabees, and just as the Suffering Servant did in Deutero-Isaiah. Since the early Christian community included many Gentile believers, the new idea was that Jesus died not just for Israel but for all mankind...Gentiles included. How exactly this expiation worked varied from author to author, and not all writers viewed Jesus' death in expiatory terms (and the concept of a "ransom" is actually a distinctly different theory). But those that did not only utilized the Suffering Servant theme to describe the importance of Jesus' death but also took the symbolism literally as a prophecy of Jesus himself. 1 Peter 2:21-25 contains four seperate allusions to the Suffering Servant poem ("There had been no perjury in his mouth," Isaiah 53:9, 1 Peter 2:22; "He was bearing our faults in his own body," Isaiah 53:12, 1 Peter 2:24; "through his wounds you have been healed," Isaiah 53:5, 1 Peter 2:24; "You have gone astray like sheep," Isaiah 53:6, 1 Peter 2:25), and the gospels are similarly filled with references to Isaiah 53. Some examples:
"This was to fulfill the prophecy of Isaiah: 'He took our sicknesses away and carried our diseases for us' (Matthew 8:16-17; cf. Isaiah 53:4).
"Because I tell you these words of scripture have to be fulfilled in me: 'He let himself be taken for a criminal' (Luke 22:37; cf. Isaiah 53:12).
In fact, even the plot and specific scenes in the gospels are based on the Suffering Servant and OT laws on the scapegoat ritual. Thus Jesus was silent "like a lamb that is led to the slaughter-house, never opening its mouth" when he was being accused (Matthew 26:63; cf. Isaiah 53:7), and like Jesus the scapegoat ritual included a crowning of red wool on the victim's head and being put among thorns (cf. the scarlet/purple robe and the crown of thorns), and being spat upon and pierced with a reed (cf. especially Barnabas 7:7-11, which is most explicitly based on scapegoat traditions in Leviticus 16, and the Gospel of Peter). Even the hand-washing scene with Pilate and the mob in Matthew 27:24-25 is based on the expiatory sacrifice described in Deuteronomy 21:6-8 LXX.