What Hinlicky criticizes in the book is the tendency of the Church Fathers and the larger Christian theological tradition to think in terms of divine simplicity. Hinlicky is basically incorrect as to the proper definition of divine simplicity. As Richard Muller points out, all divine simplicity actually means is that God is uncompounded. God isn't "made up" of any antecedent qualities. Goodness, holiness, and all his other qualities don't some how come together to form God. So, actually divine simplicity is really just a function divine aseity. Hinlicky claims that divine simplicity means that there is no differentiation or distinction in God (this is a common misunderstanding). Hence, (according to him) it rules out the Trinity or makes the divine ousia a 4th thing alongside the three persons. He sees the genesis of this sort of thinking in the Platonic philosophical tradition that sought to critique the Homeric pantheon by erasing any differentiating qualities of the gods. By doing this, one arrives at an essentially transcendent, unknowable, and undifferentiated God.
In contrast to all this, Hinlicky wants to talk about divine "complexity," wherein God is properly defined as a complex of love, manifested and actualized in the three persons of salvation history. The reality of the three persons is constituted by their action in salvation history, wherein they "anticipate" the fulfillment of their reality as it will be actualized at the eschaton (similar to Jenson). Hinlicky finds this way of thinking about the divine being present in the Gospel tradition and the other authors of the NT.
To make a long story short, early Christian thinkers tried to mix these two paradigms together. As a result, they developed an unstable mix and drifted towards subordinationalism (Origen is the best example of this). Of course, subordinationalism as Origen taught makes no sense. If Jesus is God and possess the fullness of the divine substance, then how could he at the same time be less than the Father? How can God be less than God? This unstable mix broke apart at Nicaea and created two exclusive position: Arius wanted a pure divine simplicity. If that was the case, then God had to be frozen in eternity, and therefore couldn't interact with reality. If he did, his transcendence and simplicity would be threatened by entering into the world of differentiation and mutability. By contrast, the Cappadocians understood God's reality as something as dynamic and living. The unity of the divine ousia could be found in the coherence, and unity of the life of the three persons, rather than an abstract, undifferentiated ousia beyond being.
For the most part I think that this account has much to offer. I have many criticism of it historically, but I'll bracket those for the moment. Theologically, I find the argument a bit cliched. Much of modern theology with its Hegelian metaphysics attacks classical theological categories like "simplicity," "immutability," and so-forth, simply because they don't allow for a certain kind of divine imminence in history. This sort of thinking usually results in a God who evolves himself through the means of the historical process.
The problem with this is several fold. First, for all the complaining about Greek metaphysics as all these theologians do (Jenson, Braaten, Moltmann, Pannenberg, Jungel, etc.), their main modus operendi is to simply replace Greek metaphysics with German Idealist ones. Their metaphysics have as little to do with the metaphysical presuppositions of the Bible as those of Pseudo-Dionysius. Secondly, as David Bentley Hart has noted, making salvation history about divine self-development actually makes God deeply selfish and therefore is contrary to picture of God in the Bible. If God is immutable, and contains every possibility within himself already, then creation and redemption are pure gratuity. They exist because God gracious wants them to exist . God doesn't need them as a means of self-development. If you say that God does need them for this purpose, not only does creation somehow offer possibilities which God doesn't have (an odd claim!), you also posit that God made the world for his personal self-development. Hence, the world exists not out of grace, but to help God achieve his egocentric goals.
A better critique of Arius and Plato, and the entire tradition of Platonic metaphysics can actually be had through the lens of law-gospel. This does not mean abandoning divine simplicity and immutability, but rather rejecting the Platonic interpretation of these divine attributes.
Plato wanted God or "the Good" to be frozen because he wanted the law to be stable. In a word, the Sophists made a mess of public morality, claiming anything was a true because good rhetoric made it so. Plato wanted to say "no, the Good is stable. It doesn't change based on rhetoric." Hence, God is law and he can't be anything else. For human beings, this is an attractive proposition. If God is only law, and he must obey the law. He can then be controlled by the law. Similarly, Arius did not want to compromise the law either. He taught that Jesus saved because he was a good model. He showed how creatures could achieve salvation by corresponding to the law. Hence, if God was not an utterly static being and could in fact change his relationship to creation, then the law would be disrupted and so would the possibility of human salvation through it.
Though Athanasius did not reject God's immutability, he did insist that God could change his relationship to his creatures. Hence, God was not only law, but also gospel. God come change his relationship with his fallen creatures by becoming incarnate and redeeming. In doing this, he overcame the dark powers of the old creation. This ability to engage in self-giving was rooted in God's own Trinitarian life. God was by nature, according to Athanasius and the Cappadocians, self-donating and communicating. Just as God communicated himself in the procession and begetting of the Trinity, so he communicated his glory to humanity through Jesus. Hence, God's immutability was more to be identified with the infinity and constancy of his life (fire not ice!). God possesses all and can give all in his act of self-communication. Hence, creation and redemption can be purely gratious. They give nothing to God- he is free within himself to act according to his grace.