Middle-Endian is how it tends to be said out loud in English. Even in countries that would write 25/3/23, you still usually answer "What day is it?" out loud with "It's March 25th" rather than "It's the 25th of March." And after that point, the year going at the end makes sense because people are generally not asking what year it is. The only thing that makes it confusing at all is Europe choosing to do it differently without a clear way to tell which system is being used in some cases (you could say this about timezones as well, and would be right to complain there as well, but that doesn't mean that someone's particular timezone is "more correct").

In my opinion though, using a number for the month at all is silly. Nobody ever answered "What month is it?" with "Five." A better format would be to use standard 3-letter codes for the month, e.g. MAR:25:23.