The more important question is whether what Akerlof and Shiller have offered in Animal Spirits amounts to "a theory" in the sense that it could stand in place of the current theories that they criticize for being based entirely on rational responses to economic motives. There is a difference between a series of ideas about different aspects of economic behavior and an integrated account of macroeconomic fluctuations. Akerlof and Shiller are surely on the right track in pointing to elements that are missing from today's conventional models, and in arguing that incorporating them into mainstream macroeconomic analysis would help. But they have neither done this nor shown others how to.
In fact, it's worse than that. Here's Friedman a few paragraphs earlier:
[F]or purposes of macroeconomics—the study of the economy as a whole—most of the standard models do not admit the possibility of unemployment. The reason is not that no one knows unemployment exists. Rather, no one has figured out how to allow for it within the confines of sufficiently simple mathematics; and faced with the choice between excluding unemployment and sacrificing analytical simplicity, most macroeconomists have opted for the former.
But "Opted" suggests they had more of a choice about it than I think they did (or do). Tractability is essential; without it, you have laundry lists of effects that you can't quantify, like Akerlof and Shiller. On the other hand, if the price of tractability is complete irrelevance, that's problematic too. What makes people think macroeconomics is solvable?