I should perhaps have said in the OP that I understand the natural examples perfectly well; what startles me is that here I'd expect certain exogenous factors (the introduction of income tax and its later peak and descent, the rise and fall of the automobile industry, World War I and the Cold War, etc) to have some significant effects on the growth rate, and different effects in different eras.

Instead, it looks to me (with the exception of the Great Depression and recovery) like the growth rate never leaves the 3-4% range, once you average over decades to iron out the fluctuations. I noticed that this confused me.