I've settled on the explanation that this is just a cultural difference, and anyone arguing from a place of "logic" or "correctness" is refusing to accept that it's all convention, and different people do things differently.

As an analogy, some languages put the verb at the end of the sentence (e.g. Latin, certain German grammatical structures). As an English speaker, this is weird because I don't really know what's going on until the sentence is done, and it feels like I'm putting together a little puzzle in my head. Whereas to a fluent speaker, it presumably just makes sense and you don't really find it difficult. Same thing with dates.

As an American, I like our convention for writing dates. I usually care about month first. Immediately upon seeing a date, I know the rough time frame. Is it this month? Next month? Around Christmas? Around my birthday? Then the day pins it down to something specific. I will assume a date is referring to the current year, unless I see a different year, in which case it's a quick update to my mental model. April 12 flows as "soon, and exactly 18 days away" and September 12 flows "far away, and the middle part of the month".

I get that computers are a different use case, and there I'm a ISO 8601 advocate.