The doctrine that God is identical with his nature has traditionally been defended by Christians, and would be useful for responding to the following argument (defended by Quentin Smith, Wes Morriston, etc.):
(*) The best answers to the problem of evil all involve significant libertarian freedom; but significant libertarian freedom is not something God has (because he cannot do wrong); a freedom that God does not have is not the most valuable kind of freedom; therefore, significant libertarian freedom is not the most valuable kind of freedom.The challenge this argument presents is to come up with a reason to think either (a) that significant libertarian freedom is valuable in us, but would not be valuable in the case of God because of some relevant difference between us and God, or (b) that God has a kind of freedom which is more valuable than significant libertarian freedom, but it is a freedom that we cannot have. Both kinds of responses (actually, they may not be very different) require the identification of a disanalogy between us and God. One proposed disanalogy is that God is identical with his nature, while we are not. Therefore, actions that are necessitated by God's nature are rooted precisely in God. But we are not identical with our natures, and hence any actions that were necessitated by our nature would be rooted in something outside of us, contrary to source incompatibilism.
One of the next moves in the dialectic (Wes Morriston does this) is to question the coherence of the doctrine of divine simplicity that the identity of God with God's nature is based on, giving standard objections such as asking how God's attributes could be identical (e.g., how could God's omnipotence be identical with God's mercy?) However, although I have tried to answer such objections, I think this is not how the present dialectic should go. For the doctrine that God is identical with God's nature is not the doctrine of divine simplicity--it is only one of the entailments of the doctrine of divine simplicity. Thus, it is prima facie possible to defend the identity of God with God's nature without defending the doctrine of divine simplicity. Perhaps in the end one can derive divine simplicity from the identity of God with God's nature. But those are going to metaphysically controversial arguments.
So, how might one defend the identity of God and his nature? Well, let's ask what the alleged difficulty in that identity is. I see three metaphysical difficulties, actually: (1) Could anything be identical to its nature? (2) Even if so, could anything concrete be identical to its nature? (3) Even if so, could anything causally efficacious be identical to its nature?
The first difficulty has a neat answer, assuming each thing has a nature. To rule out regress or circularity, we must hold that there are things that are their own nature, and hence that such things are possible. Both the Platonists and the Aristotelians believed in such things: Plato held that the Form of Goodness is its own Form and Aristotle held that while there might be a difference between Socrates and his essence, there is no further difference between that essence and the essence's essence. I do not know of any generally accepted, or even very strong, argument against this part of their view.
To press the second difficulty requires an account of the notoriously difficult distinction between the concrete and the abstract. Of course, if one identifies the concrete with the physical, then one has such an account, and a negative answer to (2) appears plausible. But if one identifies the concrete with the physical, then a negative answer to (2) is irrelevant to the question at hand, because then God is not concrete (apart from the Incarnation). One might identify concreteness with particularity, and insist that natures are universal. But then one needs an account of particularity and universality. I take "particular" to be one of a pair of coordinate terms, any given particular being understood as particular in relation to a universal that is predicated of it. But on that story about particularity, there is no reason why something couldn't both be particular and universal: greenness is universal relative to foliage and particular relative to being-a-color-property. There is nothing even obviously absurd about the idea of something being a particular and a universal in relation to itself. Thus, propertyhood is a particular in relation to itself--as it has the universal propertyhood--and a universal in relation to itself--as it is had by propertyhood. I think the only plausible way to expand on particularity that makes (2) problematic is by saying that the concrete is what stands in causal relations. And that leads to (3).
Could a being identical with its nature be a cause? Here is one argument to the contrary: No non-material being can be a cause, and no nature is a material being. But if the first premise of this argument is established, then theism has been ruled out--there is no need to go for the problem of evil then. Anyway, I see no good reason, apart from some clearly false Humean accounts of causation, to suppose that causation is limited to material beings. Or maybe one could say that natures are abstract, and abstract things can't be causes. But why not? One could stipulate this, making acausality be a part of abstractness. But then the negative answer to (3) is trivial, and the substantive problem shifts to the question whether natures are abstract.
Moreover, again both Plato and Aristotle posited causally efficacious things that were their own natures--the Form of the Good is responsible in some way for the shape of things, and the nature of Socrates has biologically formed the adult Socrates from childhood. There has been ample time for the production of a solid argument that this part of their views is incoherent or otherwise impossible. Maybe there is one that I don't know of. But unless one can be produced, the presumption is that a negative answer to (3) has not been proved.
There is, however, a different dialectic move that can be made. It is to argue that apart from divine simplicity, positing the identity of God and God's nature is ad hoc and brought in just to answer objection (*). But I don't think so. For there is a good argument for the identity of God and God's nature from four premises: (i) everything distinct from God depends on God (a central theistic belief), (ii) dependency (in sense that is found both in (i) and (iii)) cannot be circular, (iii) everything that is distinct from its nature depends on that nature, and (iv) everything has a nature.