LOVE that question, reader Molly. Indeed, a mixture of melted butter and flour should in theory have plenty of thickening power just the way it is. Why bother to cook it? The primary reason is texture. An uncooked roux yields a thick sauce, but one that has a vaguely mealy mouthfeel. That’s the result of the flour granules in the mix, which are big enough that they register on our tongues. The result is sometimes described as a “starchy” taste. A few minutes’ exposure heat causes the flour particles, which are nothing more than bundles of stick-like starches, to start shedding molecules. As that happens they reduce in size to the point that we can no longer detect them.
The interesting thing is that as you continue to cook a roux, and the flour granules get ever smaller, the thickening power of the roux goes down (for reasons that are explained here). Still those styles of roux have uses, especially in the world of New Orleans creole cooking, which sometimes calls for roux that’s cooked to near blackness. I don’t know what purpose those deep dark things serve, but I’m sure someone somewhere out there will enlighten me. Thanks again for the question, Molly!