The problem discussed in Danielle Allen's book is that Socrates explicitly says in Phaedrus that dialectic, i.e. inquiring discussion, is the road to knowledge, and that writers, such as Homer, cannot do this work. And yet Plato, Socrates's admirer, chose to write philosophy. Why?
Allen proposes that Plato realized he needed to reach more people to effect the political changes he wanted. This could only be done by writing, and writing effectively, through crafting concepts, images and messages that were pragmatically efficient at transmitting the underlying ideas. Plato's excuse for using writing in spite of Socrates stance is basically that writing is a form of the noble lie, a statement that is not true, but still gets the job done. Plato was the western world's first message man, giving the politicians after him ready-made sound-bites.
I find Allen's approach intriguing, although a bit thin as regards the evidence for some hypotheses. The sources are few; much that surely would have been relevant has been lost in the mists of time. Allen makes good use of what there is.
It is somewhat interesting that Allen dismisses Popper's analysis of Plato as a totalitarian in a single sentence. I would like to ask Allen in what way her analysis conflicts with that of Popper. In my view, they are wholly compatible.