ISO 8601

That's locality of reference, though, similar to how you can say "here" or "there" for spatial coordinates. Everybody is aware of the year and month, so you omit it as given. The order of significance is still year, month, day.

Imagine if a harried time traveler jumped out of their time machine and asked you the date. Would it make sense to say, "Why, it's the 1st." (Or more possible, if a friend awoke from a coma.) If you ask somebody when they were born, most people will give the year at minimum. Of course, there are some weirdos out there, and you recognize them when you ask when they were born, and they say, "on a Tuesday." Same for the date of the Norman invasion of Great Britain. If you don't already have some sense of history, then knowing it happened about the 20th isn't very edifying.

Writing dates is usually in order to keep track for the future, when the year and month may be different.

I used to work for a company that agreed with you, well at least some clown in management did. Even though it was an Australian company, at least part of the problem was we had an office in Manila, and they speak "American English" which seemed to include the awful date system too. We dealt with a lot of files being issued to clients / received from vendors etc. Because the "official" system used those fucked up dates, everyone ran their own secondary sets of data folders in / out with everything done in ISO dates so you could actually sort it properly.

Which I was the justification used when my work decided to use 2025-May-01.

It’s close enough to the iso date that nobody will be confused but with that 1 extra layer of security blanket to separate months and days.

Of course, that does ruin sorting, so I think it was a bit silly, nobody has ever used yyyyddmm so it’s all a bit theoretical to me.

27 Feb is no more or less ambiguous than 02-27. The problems are when you choose a proper example, like 03/02