Does Christianity limit God? I'm sure you're familiar with the other theories of the atonement. Satisfaction and Penal Substitution are only two, closely related, versions explaining what Jesus may or may not have done. There are a few others, even within the Western traditions. For instance, the earliest view of salvation/atonement was the idea that God paid Satan in order to redeem humanity. The idea is that Satan had laid claim to human souls through our rebellion in the Garden of Eden and therefore God could not simply forgive sinners but had to purchase them back from their post-fallen ruler. Jesus is this payment. However, since Jesus was a perfectly sinless substitute, Satan could not hold him and he was thus freed.
My other favorite is the Cristus Victor theory which suggests that God in Jesus was challenging and transforming the evil powers of the world through his life and ministry. This doesn't have a payment or a satisfaction to make, but is more of an example by which God would win over the world to be more merciful and peaceful.
There are other examples, but this doesn't really get to the heart of your question which is about the nature of God based in a specific atonement theory. My point in bringing these up was to show that Christians do not agree on the life and meaning of Jesus, especially throughout history.
But, if God did need a perfect substitute in order to fulfill justice and assuage wrath, then He would be limited, but only by His nature. The Christians I know who hold to this position, and I used to be one of them, claim that nothing external to God has ultimate authority over God. This is what omnipotence means to them. So, if God were to be limited in needing a sacrifice from Jesus to fulfill the Adamic covenant, the covenant the Adam and Eve broke, then this theistic model would say that it is only God's nature that limits Him. Gos is simply appeasing Himself. It cannot be within God's nature to have an external authority.
I do not hold to this view as we see Jesus forgiving sins without a perfectly just payment all the time in the New Testament, not to mention that this God is entirely fearsome. I hold that God can indeed simply forgive people, but this is because God's nature allows it. Your question is a good one because it gets to the heart of who we think God is.