I don't have any real "case" for it, but those terms seemed to be associated - in the minds of the generation before me - with prohibition and "mobster" code or jargon. The most common use I saw of the terms in the 1940s thru 50s was in comic strips where the person using them was implied to be of "less than upstanding" reputation.

An alternative explanation was that "naming" the notes made it easier for people to make transactions between and among mixed immigrant cultures with different languages. That might imply a much earlier origin and usage(?).

I knew a few whole families, 1950 - 1960 era, who were so "arithmetically challenged" that they simply "didn't know the numbers." One woman who worked during that time for my father's business always asked him to cash her paycheck for her, which he did for a couple of years before she explained that she didn't know how to write her name, and he learned a little later that she could name her kids (7) but couldn't tell anyone how many there were - i.e. couldn't count them. (The Deuce, Fin, Sawbuck, etc terminology might have been "helpful" to her and her family, but it was so little used by that time that nobody thought to teach it to her.)

John