Have another go at this train of thought, mate... You're basically saying "MM/DD" is better at sorting chronologically than "DD/MM", since the year part is taken out of the equation, which is already the established consensus, and not ironical whatsoever. And the ISO standard is already to use YYYY-MM-DD, so that's the winner IMO, hands down. Japan is simply following that but using a slash as the delimiter.
When you search or do any stable sort, I would think you want your primary attribute to be the one with most finite values? That way you are front loading the pruning of the search space.