So, the crucifixion is just him putting the right cover page on the TPS report*? He'd included this bureaucratic requirement for anyone wanting to submit an atonement request for processing and he felt obligated to go through the same procedures himself? This is how I'm understanding your response. Please let me know if that's an incorrect understanding.
If that's the case, it still doesn't make much sense. The sacrifice is somebody asking God to do something which he would not have done absent the request. In the case of the crucifixion, there's nobody involved except God, so his forgiving everyone is just him doing something he was going to do anyways, since he was the one making the request. Nobody's asking anybody else for anything they weren't planning on doing anyways here, so it's not really a request in the first place.
Now, even if we view the crucifixion as some red tape that God just didn't want to cut through, how does Jesus's suffering fit into it? I'm not familiar with ancient Jewish sacrifice rituals, but did they need to make the goat scream? Did the sacrifice involve making the goat die slowly and painfully over the period of several days or did they just cut its throat and have it bleed out quickly? I'm assuming it was the latter. People are always making a big deal about how thankful we should be to Jesus for going through all of this suffering for us, but that carries with it the implication that this suffering was somehow a necessary part of the process and the atonement would not have happened if Pilate had had some random soldier smother Jesus with a pillow while he was sleeping. If it's simply Jesus filling in for the goat, why would the method of his death and how much pain he goes through during it be relevant?
* This is an Office Space reference in case you didn't get the meaning of the line
Okay, most of what you have asked here is covered by the extended explanation I wrote - so here is the whole thing:
The first thing I need to establish is we have not been told why God determined that blood sacrifice was required for forgiveness; all the scripture states is that this is the standard He chose and abides by as He will not contravene his own covenant with man. Leviticus 17:11 tells us what reason God used for this: “For the life of a creature is in the blood, and I have given it to you to make atonement for yourselves on the altar; it is the blood that makes atonement for one’s life.”
This is also stated in Hebrews 9:18-22 “That is why blood was sprinkled as proof of Christ’s death before even the first agreement could go into effect. For after Moses had given the people all of God’s laws, he took the blood of calves and goats, along with water, and sprinkled the blood over the book of God’s laws and over all the people, using branches of hyssop bushes and scarlet wool to sprinkle with. Then he said, 'This is the blood that marks the beginning of the agreement between you and God, the agreement God commanded me to make with you.' And in the same way he sprinkled blood on the sacred tent and on whatever instruments were used for worship. In fact we can say that under the old agreement almost everything was cleansed by sprinkling it with blood, and without the shedding of blood there is no forgiveness of sins.”
The first blood sacrifice in the Bible is noted in Genesis 3:21 when Adam and Eve were expelled from Eden: “The Lord God made garments of skin for Adam and his wife and clothed them.” This was done to impress on them the consequences of sin and show them death so they would know what they faced due to their disobedience.
When God gave the law to Moses after the exodus, he established the standards for the annual priestly sacrifices at Passover. The sacrificial offering was to be a perfect animal or bird, with no visible blemishes. Every family was to participate in this on the annual basis for forgiveness of their sins over the year. It was also intended to remind them of the cost of sin just as the first sacrifice did.
But the annual sacrifices were not a permanent atonement and had to be repeated since the sacrifices were not actually perfect; they only appeared perfect. They are considered a foreshadowing of Jesus' sacrifice on the cross. This is explained in Hebrews 10:1-14. Verses 3 & 4 are particularly on point for this: “But those sacrifices are an annual reminder of sins. It is impossible for the blood of bulls and goats to take away sins.” In addition to this, it was not possible for Gentiles to participate in these rituals as they were forbidden to enter the temple grounds sacrificial area. So it was not only temporary in effect, it was also limited in scope.
Jesus' incarnation was God's chosen method of permanent atonement for man's sins. He lived a perfect life and offered Himself as the perfect blood sacrifice as atonement for all who accept Him as savior. As we discussed before, the method of his death was to fulfill prophecy regarding the manner of his death.
All of this is pretty standard mainstream theology, and is usually the basis offered as an explanation of the reason for the incarnation.
As for the suffering part - no, that was not a requirement for sacrifices. As you are probably aware kosher food has as one requirement that the death be as painless as possible. Since the ancient Jewish priests ate part of the sacrifices, this requirement would also apply to those animals. Typically their throats were slashed so they would bleed out quickly. But the suffering of Jesus on the cross was again necessary to fulfill prophecy about his death.
Hope this answers your questions. Let me know if it doesn't.
Ruth
Edit for clarification: The final paragraph regarding suffering was not part of the original response I had composed. I added that to answer a specific question you asked in your post.