One day at La Rochelle, while waiting for the Machado girls who used to keep me company every morning on my way to the lycee, I grew impatient with their lateness and, to while away the time, decided to think about God. "Well," I said, "he doesn't exist." It was something authentically self-evident, although I have no idea any more what it was based on. And then it was over and done with...Similarly with microfoundations: First of all, they don't exist. But this rather important point tends to get lost sight of when we follow the conceptual questions too far out into the weeds.
Yes, your textbook announces that "Nothing appears in this book that is not based on explicit microfoundations." But then 15 pages later, you find that "We assume that all individuals in the economy are identical," and that these identical individuals have intertemporally-additive preferences. How is this representative agent aggregated up from a market composed of many individuals with differing preferences? It's not. And in general, it can't be. As Sonnenschein, Mantel and Debreu showed decades ago, there is no mathematical way to consistently aggregate a set of individual demand functions into a well-behaved aggregate demand function, let alone one consistent with temporally additive preferences. So let's say we are interested in the relationship between aggregate income and consumption. The old Keynesian (or structuralist) approach is to stipulate a relationship like C = cY, where c < 1 in the short run and approaches 1 over longer horizons; while the modern approach is to derive the relationship explicitly from a representative agent maximizing utility intertemporally. But since there's no way to get that representative agent by aggregating heterogeneous individuals -- and since even the representative agent approach doesn't produce sensible results unless we impose restrictive conditions on its preferences -- there is no sense in which the latter is any more microfounded than the former.
So if the representative agent can't actually be derived from any model of individual behavior, why is it used? The Obstfeld and Rogoff book I quoted before at least engages the question; it considers various answers before concluding that "Fundamentally," a more general approach "would yield few concrete behavioral predictions." Which is really a pretty damning admission of defeat for the microfoundations approach. Microeconomics doesn't tell us anything about what to expect at a macro level, so macroeconomics has to be based on observations of macro phenomena; the "microfoundations" are bolted on afterward.
None of this is at all original. If Cosma Shalizi and Daniel Davies didn't explicitly say this, it's because they assume anyone interested in this debate knows it already. Why the particular mathematical formalism misleadingly called microfoundations has such a hold on the imagination of economists is a good question, for which I don't have a good answer. But the unbridgeable gap between our supposed individual-level theory of economic behavior and the questions addressed by macroeconomics is worth keeping in mind before we get too carried away with discussions of principle.