That's actually the theory of the origin of the split, believe it or not, formal vs casual tone in writing and speech.

British papers would print the current date as Fifth of September or whatever, American papers would print it as December 18th. There's exceptions in the record for both, obviously, but that's the leading theory last I heard.

There's also a bit about the British papers being more readily available so more people read it daily and the day was more important, versus American papers having a more rural audience where the month was more important and daily events not so much but I'm not sure I buy that one.