FWIW, I went back and looked at some of my research on chip sizes in the early days of mass production of composition and “ “paranoid” chips made specifically for poker c. 1880-1910. (When chips were bone, ivory, mother-of-pearl, etc., sizes and shapes were all over the place.)
A lot of the best and most comprehensive evidence available can be found in U.S. advertisements and catalogs.
These show chips for sale varying from as small as 7/8” to seldom if ever larger than 1-5/8". (I’ve seen exactly one sales pitch for 1-7/8", or 41.275mm, though tiny fractions are sometimes hard to read in repros of old ads.)
Throughout this period, but especially on the earlier side, 1, 1-1/4, 1-1/2, 1-5/8" and 1-9/16" inches are the most common sizes with the occasional 1-3/8
1-9/16ths is about 39.68 mm, whereas 1.5 inches is more like 38.1.
By 1900, you start seeing more ads referring to these two sizes as “full” or “regular” size, depending on their type. (Paranoids, for some reason, seem ti have been mainly 1-9/16ths.)
Seymour’s catalog has a lot of ads toward the back if anyone wants to check this out.
The convergence on a size midway between these two seems to have come over the next few decades, especially as Nevada casinos started commissioning “clays.”
The one thing that’s clear is that as far back as 120-140 years ago, almost all of the big chip producers were hovering around the current standard, up or down not much more than 1/8".
I would add as a conjecture, though ads reflect this somewhat as well—that once the over 38/under 40 standard was set, other factors besides usage and familiarity probably came into play… For example, if a host or room already owned chip holders, trays and racks which fit existing ~39mm chips, that would have created another obstacle to any serious size change, whether up or down.
One thing seems clear, though, that apart from bone chips and plaques, “cheques” over the size of 38-40mm were exceedingly rare.
I’m not sure if today’s ever-increasing sizes are the result of the need for greater “bling” on TV… Or chip manufacturers wanting to create new products they can market after big casinos already bought their main chipsets… Or just people being bored / wanting variety / always thinking bigger is better.