In my PhD viva, the external examiner pushed me on one question in particular: what does the drama of Plato's dialogues add to his philosophical arguments? I responded that it carries his readers with him, so that they do not just rationally engage but are emotionally moved too. That way, Plato's philosophy gets under your skin; it might change you. The examiner was not really persuaded: why shouldn't an abstract argument move you too, if it is rationally convincing? I think I came back with the thought that we are not only or ultimately rational beings, and so philosophy, as the love of wisdom, not merely the construction of a good argument, needs means other than just logic. But schooled in the analytic tradition, the examiner did not buy such a broad definition of philosophy.
I think this sugestion is right; Plato's dialogues are not merely descriptions of arguments. They are (so to speak) ways of acting on the reader. Just as part of the purpose of Bunyan's Pilgrim's Progress is not merely to lay out Christian life but to impress upon people the way out of the City of Destruction and into the Heavenly City, so are Plato's dialogues not merely catalogues of arguments in dramatic form, but instruments for transforming sophists into philosophers. But I think there is yet another thing that the drama gives us that could not be had by simply stating the arguments: Socrates. And Plato's Socrates is at least as important a contribution to philosophy as any argument Plato puts in his mouth.