What I like about it is that it arranges things in order of importance/relevance in most situations. The month tells me the most important bucket, the day clarifies the particulars, and the year locks down the date but it is almost always known in the given context. In my opinion, there is the one true format for data formatting and text representation (the ISO standard), but each of the various permutations do have their use cases where they shine. For normal dates, all three components are needed, but it is usually nice to know the month, then the day, and then the year is there just to be clear. Knowing the day gives me little information until I have the month, whereas getting the month first gives me more information, where sometimes I can even ignore the day.
In my experience, the thing which is the most important/relevant in most situations is the day of month. People often say things like "dia 10" when asked when something is going to happen; that means in context the 10th of the current month if today is the 9th or earlier, or the 10th of the next month if today is the 11th or later. The month is added only when necessary, like "dia 10 de fevereiro" (just "dia 10" today would mean the 10th of January).
When are we back at work? On the second. Then go-live is on the fifth of March. (Normally 5 March or 5th March when written.)
Are you telling me if you had file cabinets for the last 50 years, and you had to get a specific file Nov 1992, you would rather sort first and get all the files marked "November", and then sort through those 50 to get to the 1992 November? Surely one would reduce down to the year - 1992 - first, and then to the month.
Same for alphabetical ordering, a data list ordered by logname-MMDDYYYY.log alphabetically wouldnt be chronological order - YYYYMMDD or DDMMYYYY would.
Month is primary in some cases sure, but I think year and day endian are primary in many others - plus have the above sorting and ordering benefits.
> each of the various permutations do have their use cases where they shine
The evolution of the US ordering feels (I might be wrong!) similar to how spoken numbers are little endian from 11 to 19, yet big endian from 21 to 99. Some languages are even worse in this regard; but regardless, they're unhelpful historical artifacts that we learn to live with, not actually helpful, well-thought-out, or even merely irrelevant. Notably there are considerable differences between how quickly children learn maths in different languages, and digit ordering may contribute (of course other cultural factors may contribute too). I wouldn't be surprised if date ordering too is similarly a small but real drag on learning.