Speculation: Perhaps in 1960 businesses were really distributed according to a power law but have reapportioned a bit over time. Trends like consolidation and dominance of a few large firms might skew things.
That's like measuring the heart rate, LDL, HDL, blood sugar level, systolic and diastolic blood pressure, height, weight, hair length, number of children, salary, home value, and total miles driven on all of the cars... of an entire football stadium worth of people.
And it's not like he's correlating these numbers, that your salary is proportional to your home value, or your weight is proportional to your blood pressure.
No, these are statistical properties of the numbers themselves.
The hypothesis of the paper is that statistical deviations correlate with financial crises. You doubt that correlation, but you think all of thousands of other numbers can credibly show a statistical correlation? :)
Basically, Benford's Law works where the values are an open-ended count of something. When it's a measurement within a bounded domain, all bets are off.
Try centimeters.
*(of course some companies like Berkshire Hathaway are famously okay with that.)