ISO-8601 only really applies to the Gregorian calendar.
[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.
* "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
(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'.