I think we need to go back further. The law came from someone. When Jesus saved us he saved us from himself.
Oh boy, here we go.
That seems crazy. But we've got to understand that it was God who was most offended by sin.
It seems crazy because it's philosophically ridiculous. It signals a terrifically inconsistent understanding of the nature of God.
God is the one who judges. God is the one who pours out his wrath on the ungodly. It is he who sends them to hell. It is he who made the law. God is the offended party.
Let's think about God for a second. As God is God, God is just in whatever God does, correct? That is, God could do whatever human minds might understand as "sin", but God's doing it would still be perfectly justified because God can only do good, since the determination of God's "goodness" is not based on what God does, but who God is.
In the same way, we must think about God's justice. If God is just, it is not because God does "x" or "y" in order to demonstrate divine justice, as if the determination of God's justice were made by God's alignment with some standard external to God. To the contrary, the justice of God is demonstrated precisely in who God is, e.g., God.
In this way, whether God damns every single human to hell for the fun of it, or pardons all of humanity because of indigestion, God is perfectly "just" in either (and both) scenario. This is a necessary conclusion, as God's justice is based not upon the alignment of God's actions with a standard of "justice" which is external to God, but rather because God is God, and is therefore necessarily just.
Because of this conclusion, the notion of the necessity of God doing "x" because God is "offended" by sin is
fundamentally absurd. Whether God arbitrarily self-flaggelates Godself, or simply laughs and "gets over it", there is no necessity for God to act in any particular way in response to human sin. Each response would be equally just and perfectly in keeping with God's holiness, given that God's justice and holiness are not based on what God does, but are terminated in the sheer reality that God is God.
Now then, with these obvious and elementary concepts established, we must move the evaluation of your proposal.
* If God is not bound by any power external to Godself to act in any particular way to human sin;
* And if God kills Godself on the cross because of human sin;
* We must necessarily conclude that God kills Godself on the cross precisely, and only, because God wants to.
Based on this conclusion, though, what picture have we made of God? I don't deny that it's a perfectly legitimate picture...after all, if God is a sado-[bless and do not curse][bless and do not curse][bless and do not curse][bless and do not curse][bless and do not curse][bless and do not curse][bless and do not curse][bless and do not curse][bless and do not curse], God is perfectly justified in being such. But I'll pass on worshiping such a God, thanks.
Yet we have something even more amazing:
"but God shows his love for us in that while we were still sinners, Christ died for us. Since, therefore, we have now been justified by his blood, much more shall we be saved by him from the wrath of God. For if while we were enemies we were reconciled to God by the death of his Son, much more, now that we are reconciled, shall we be saved by his life."
(Romans 5:8-10 ESV)
We were sinners, we were facing the wrath of God, we were enemies. Yet God made the first move! He came to rescue us from sin! How amazing is that!
But this "rescue from sin", in your own words, is really a "rescue from God" While we were still sinners, Christ died to save us from himself. Given that Christ could have simply gotten over whatever animosity God has toward humanity, he chose to kill himself to demonstrate just how neurotic the eternal God is.
Obviously, this is a different translation, but is precisely what you are advocating.
In the UK there was a famous situation of a man's son being murdered. This Christian father went on national television and told the murderer he forgave him. Despite being the one sinned against, he made the first move.
The father committed suicide (this is the logical outcome of your attempted analogy)? I'm confused...
In the same way, we have sinned against God. Yet he made the first move (and the last move and every move in between). He reconciled us to himself, though we were his enemies.
But there was no move to be made! If the problem of sin is really God's anger against humanity, the ONLY thing that needs to happen is that God simply needs to get over God's anger about sin. As I already showed, God simply popping a Prozac and moving on from divine anger over human sin is perfectly in keeping with the holiness and justice of God.
So then, if God DOESN'T do this, but goes to the absurdly roundabout way of completely unnecessary divine self-flagellation, we have to question what other neuroses are lurking within the divine nature.