Some interesting discussion and speculation. Indeed, every possible balls per pound will correspond to some diameter. And quite likely(?) the ability to measure to the 1/1000th precisely, and the obsession to do so, is a modern thing. Certainly, a standardization for tooling purposes in manufacture took place.
Though, all this could have lead to any infinite number of "standard" calibers. Somehow we came to have the more currently expressed array, .32, .36, .40, .45, .50 etc., instead of .33, .35, .39, .49, or even .25 (1/4"), .3125 (5/16"), .375 (3/8"), .4375 (7/16") and .50 (1/2") etc.
So somehow it came to be. Unimportant, I guess. Perhaps my initial question was not why we have the calibers we have (since we could have had any calibers attain common usage), but why would we have settled on the size increments from one size to the next?