Barth does all three. And he needs to do all three. He needs to because he's not doing encompassing single-circle, single-center systematic theology. He's not doing apologetics. He's arranging the articula fidei in ways that make them credibly sensible to the believer. But if he wants to do dogmatics within the scheme of cognate ecclesial sciences, he's stuck with unfilled dependencies on the other cognate sciences. Not to mention history, on which all three rely. So he does all four, and complains just like Nietzsche about having to do it all himself. (cf. BGE 45) Ah, the burdens of new philosophy!
If the redesign of theology away from seeking truth as religious philosophy, philology and historiography -- away from objectivity as well as apologetics -- has benefits for the subordination of theological disciplines to Christ, it stands to reason it still has those benefits. We're still doing "theology" and exegesis as academic disciplines. The existence of these and history as independent theological pursuits after truth (or more often, the smaller useful truths we call facts) is still a problem. We can debate whether being a religious practitioner is of benefit to theological work -- which knocks preaching as a theological form in its own right clean out of the picture. Religious rhetoric. But one cannot ignore (and we often do!) that Barth was a preaching theologian. Whatever else we haven't had, we've had The Word of God and the Word of Man in translation for quite some time. "The Strange New World within the Bible" is nothing without "The Need and Promise of Christian Preaching." It is the same in-falling Word of God, but put in the right place! Just as in FQI, Barth's "breakthrough," theology is set on the epistemological grounds of the church's metaphysics. But dogmatics is a second-order thing -- preaching is immediate.
Preaching has a need manifested by the congregation, by virtue of the fact that people show up to hear the Word, whether they believe that the pastor will speak it this week or have simply internalized the necessity in spite of the preacher. Preaching needs dogmatics, but the people don't. Preaching needs exegesis, and that's much closer to the people, because they can do it. But exegesis done without the priorities of preaching comes up with other results. It is questionable whether it comes up with the Word of God in ways that can be properly proclaimed as gospel. (Not that the preacher always does, mind you -- but if she has her eye on the gospel for these people, she will try!) The people need preaching, and preaching needs dogmatics and exegesis, but it must be argued conversely that dogmatics and exegesis need preaching!
I hear many complaints about how pastors never use the stuff we teach them in seminary (or that they were taught in seminary), and it's invariably a complaint about dogmatic or exegetical tools. They don't use the methods we taught them to deal with texts and theology -- and why? Because they're preaching, and beside that they're managing a congregation full of needs and wants and passions and complaints, fires to be put out and fires to be kindled. DId we teach them "theology" or "Bible" in ways that made sense to their jobs? Sittler talks about the "maceration of the minister," and the seminary prof must take that seriously! Method, technique, is a thing to be gotten "under the fingers," to be put way down into muscle memory and done until it can safely be forgotten while using it to think about the real task. But how often do we use the ranged dogmatic loci and plethora of exegetical approaches outside of survey courses for the M.Div. level? Even if we don't teach them for preaching's sake, how often are these taught for the sake of another task for which they serve? How do we answer "when am I going to use this in life?"