”Western-style“ dates don’t really exist: most countries use DMY, US for reasons unknown has gone with MDY, and Japan and China have officially standardised on ISO-8601 (YMD): https://en.wikipedia.org/wiki/Date_format_by_country
YMD is the only sane format. When you sort, you can sort by the year, followed by month and day. I do this a lot with folder names or log file names in directories, file system creation/modified dates don't always match reality. e.g. a folder named 2018-01-07 is entirely readable to anyone who looks at it, but at the same time easily sorted.
I think that the timescale on which humans live matters here. The year field doesn't change often, so for the everyday usecase it's kind of redundant – it's probably the current year, so specifying it first is kind of noisy[1]. But on the scale of hours, it's the minutes that are noise, because you likely care more about the hour. So I guess the most ergonomic ordering depends on the usecase.
[1] This could be different if you're, say, browsing an archive. Still, if I'm looking at a thread from 2005, that context is in my head, and I don't need to be constantly reminded of that by seeing 2005-XX-YY.
In English, at least, it used to be that a document such as a letter would begin with a date indicating when it was written, and then for dates ±1 month from that date would express relatively, like so:
* "The 10th instant" / "10th inst." = tenth day of current month indicated in date of document
* "The 10th ultimo" / "10th ult." = tenth day of month preceding the one indicated in date of document
* "The 10th proximo" / "10th prox." = tenth day of month following the one indicated in date of document
Arabic often writes dates and phone numbers from left to right. I can't speak for other RTL langauges but I can't see DMY being a problem for most people around the world. Ultimately, non-English speakers have to learn English to write code and if they want standardised dates across their systems they should use the standard of the language they're writing in.
Okay, there's what the date _is_ (on what calendar, what system of reckoning dates?), and there's how you serialize it.
(month: July; day-of-month: 2; year: 2018) -- can be serialized (written) a variety of ways, ISO-8601 Y-M-D being one of them.
However (month: July; day-of-month: 2; year: Heisei 30) is a different story, not just a question of serialization.
(month: Tamus; day-of-month: 19; year: 5778) -- yet more different.
(month: Shawwal; day-of-month: 18; year:1439)
"Western style dates" above means "the Gregorian calendar". Yes, how you write or serialize it for machine-parsing can be another issue. But dates on _another calendar altogether_ is a bigger one. Although the Japanese calendar that just has a different name for the year, but the months and dates and beginning and ends of the year are synchornized with gregorian -- not as big as the "Hebrew" or "Islamic" calendars which have entirely different months and years with boundaries unrelated to the gregorian calendars'.
