The shotgun gauge thing may hark back to the days of muzzle loading cannons which were referred to by the weight of their shot rather than the diameter of the bore.
Your former employer, the USN, is not innocent of measurement confusion. They list the Iowa's main guns as 16 inch, 50 caliber. What genius decided to measure the length of the barrel in multiples of the bore? And then use the same term that has an entirely different meaning in the small arms arena.
BTW, I most definitely do not argue to ensure everything "winds up base 10". Reread my white paper here...
A glimmer of hope
and you'll understand why powers of ten simplify, but are not the real substance of a rational measurement system.

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