Specifically, does Katherine Sonderegger's account in Systematic Theology: The Doctrine of God change how we think about the question "Why does God allow evil to happen?"
Think about the word "allow," which is really the critical word in theodicy. God is omnipotent, yet God is "allowing" this evil to take place. The omnipotent God could intervene, but doesn't. God "allows" evil to happen.
But if we remove God's power from notions of causality and will, if God isn't like Thanos with the Infinity Gauntlet, who could alter history or reality to protect the vulnerable and remove the violent, then how are we to understand the word "allow"? If God isn't a fickle, ultra-powerful being, dipping in and out of the flux of history, manipulating this event and preventing another, what does it mean that God "allows" something? And if we come to a different understanding about "allow" would this altered understanding lessen the acute pressures of theodicy upon our aching hearts and minds?
From my reading, Sonderegger says two things on this subject.
First, sadly, there is not satisfactory answer to be found here in this account in God's power. Sonderegger admits this. What Sonderegger's account of God's omnipotence does do, and more on this in a minute, is alter our imaginations when it comes to how we think about God "allowing" evil to exist. Sonderegger's account chastens simplistic visions of God sitting on a cloud twiddling his thumbs watching the Holocaust unfold. That twiddling thumbs vision is theodicy according to God-as-Thanos. And almost all of our theodicy debates exist within that imaginative orbit. So Sonderegger's work is very helpful in moving theodicy questions away from this imagination. Still, even with a non-causal account of God's power the question of why evil exits isn't fully answered. And Sonderegger is correct in admitting that it never will be. More, there's good theological and pastoral reasons to suggest that theodicy should never be answered.
Second, Sonderegger does paint a picture of how her vision of God's power relates to our pain, trauma, and suffering. In causal accounts of God's power, God sits in heaven, like Thanos, twiddling his thumbs and "allowing" evil to unfold. God sits at a cosmic distance, on the sidelines, and watches the evil happen. But in Sonderegger's account, God is the primal Fire that burns everywhere in creation, the Source that holds all things in being. Think, again, of the burning bush. That Fire exists and burns everywhere.
In this vision, God isn't sitting at a distance, watching the football game of history from the sidelines. God is, rather, intimately present to God's creatures, even in the midst of trauma, pain, and suffering. Again, God's closeness is no "answer" to the problem of evil, but it does bring God near and active in a way that causal accounts of God's power keep God passive and at a distance.
Sonderegger's word for this active closeness is "bearing." God carries and bears the pain, trauma, and suffering. "Divine Life" says Sonderegger, is "a radical and hidden Bearing of the lost creature." True, Sonderegger notes, "this is a bearing that is hidden away for most sufferers, just out of sight of those being carried along." God's power is always at work, hidden in humility: "As for the wounded on a litter, the Bearer is hidden from sight."
Sonderegger turns to the crucified Jesus as a sign of this bearing and what God is doing for all lost creatures. God's Being bears the tortured, dead body, carrying it through death to life: "Christ becomes, even in His lifelessness, a Sign: He will be with us as the Bearer who has Himself been borne." In the voice of the Crucified God we hear the promise: "I will bear you over death to life."
Sonderegger continues in a beautiful, poignant passage, connecting again God's power to God's hidden humility in the bearing of lost creatures:
This saving work is done in silence. The Humility of the Divine Power is known in this, that the bearing of the broken is done in darkness and without speech. The Lord does not lift up His Voice as He sustains the world, does not announce His Presence as He bears us from nothingness into the frail reality of creaturely life. We cannot break or explain away the silence of suffering divine things; there is no proclamation that renders such brokenness intelligible or comprehended. No, the dark mystery remains. But this whole can be borne. It can be lifted up, out of sight, out of our attention and grasp, carried in being, sustained even in this broken state, held. In the mute darkness, simply held. At times, those who have been brutalized in their lives, harrowed by what they have undergone, can speak of this quiet bearing. But often they cannot; we cannot. But we are not saved apart from them, the borne. They carry Christ, as He carries them...He carries them on His own litter, holds them in His own winding-sheet, and shelters them in the Silence that is His own Word, carried into death. There will be greater Deliverance than this, greater Hope still. We shall all be changed! But there is this consolation in the very heart of desolation: they will be silently held by the One who has tasted their bitterness, and tasted it in full.This God isn't a Thanos, sitting passive on the sidelines as we suffer and die.
This God is Our Mother, who holds us like Mary held the tortured torn body of her son.