I'd say that it is less than "terrifying" to plot the national debt on a log scale. Most numbers in economics (and in nature) vary in an exponential manner. Consider, for example, inflation, interest rates, and population growth. Nature deals in ratios; it is only human afterthought that adds units to measurements.

One incidental result of the fact that numbers tend to vary exponentially is that the first digit of a measured number is most likely 1 and least likely 9. See http://en.wikipedia.org/wiki/Benford%27s_law .