Just throwing out some "random thoughts"
When did cue sports turn to the metric system? 13mm = 33/64"
That's really close to 1/2" I've used 1/2" tools on old 13mm fasteners.
I'm thinking 1/2" was the original standard, if there was such a thing.
I'm also guessing that in the beginning 1/2" simply seemed satisfying to cue builders and players converting from a mace. No science. Just a reasonable size vs 19mm/3/4" that obscures too much ball and who can form a bridge around that? 6mm/15/64" may have been tried back then but adhesives weren't adequate to keep the newfangled leather tips on, so had to go for more surface area. Logically other problems with 6mm, like..........
I'm just thinking there's more tradition/history from "ancient" trial and error than real science behind 1/2" tip diameter.
I've been wrong before.
I think earlier today