That Terry Tao article is excellent, as usual (well, at least for math dorks - what's unusual about this one is that you don't need a very high level of dorkery

That Terry Tao article is excellent, as usual (well, at least for math dorks - what's unusual about this one is that you don't need a very high level of dorkery to grok it 100%) and the "executive summary" reason that Benford's law applies so broadly is easy to find: "More generally, it is not hard to show that if X obeys the continuous Benford’s law, and one multiplies X by some positive multiplier Y which is independent of the first digit of X (and, a fortiori, is independent of the fractional part of log_10(X)), one obtains another quantity X' = XY which also obeys the continuous Benford’s law." In other words, multiplicative combinations of (independent) quantities will inherit Benford's law as long as any one of the quantities obeys it on its own, so it just takes one sub-factor that grows exponentially in order for an entire distribution to follow the law.