If one remembers that the subconscious makes up approx 80% of the brain[0], there is a lot of problem solving potential in switching off the conscious and "backgrounding" problem solving to the subconscious. Which in a way, the author is indirectly describing. Engaging in activities that are "automatic" (e.g. showering, long walks) also allows the conscious to drift and frees the subconscious to interrupt the conscio…
if the brain is actually a biological neural network then this is not surprising. input takes time to propagate through the layers of the network and sleep is a necessary part of how that biological process works so the information needed to solve a problem might take a nights sleep to propagate to the depth where it can be solved or it might need a variety of other inputs that take time to acquire before enough information is ingested to reach a solution.