Idiosyncratic? Of course. People in different countries speak differently. Every natural language is totally arbitrary and “idiosyncratic”. What is your point?
The assertion that most people and most countries in spoken language say “day [of] month”, which I find anecdotally accurate, although that’s mainly in European countries and languages
This matches why almost every country in the world uses “d/m/y” in normal usage.
If you were aware of the mind-boggling diversity of human language you would not make claims like “typical languages do X so one that doesn’t is idiosyncratic” (unless backed by serious research spanning the thousands of known languages). You would also not think experience with a few languages from the Indo-European family is generalizable.
Standard Chinese for example uses Y/M/D and I’m sure you can find many examples of other formats.