But of course for full context, Americans say "March 5th, 2024", yielding "3/5/24" or similar atrocities.
I'm a big fan of ISO 8601. They got this one right. It's clear, non-preferential, and (critically) it sorts lexically with expected results!
For spoken communication you could even extend it to "Anno Domini 2024 March 5th", following the common pattern in spoken language of adding somewhat redundant filler to indicate something worth paying attention to is coming up.
Gregorian Anno Domini 2024 March 5th. :)
Because you're falsely equating "important" and "significant". It's not about little endian vs big endian, which is all about magnitudes. Most of the time, the year is implicit (i.e., this year, or perhaps next year but that will be inferred from the month). Rolling over months happens quite often, rolling over years is rare. And in cases where the month really doesn't matter, it'll be dropped: "see you on the 5th!"
That said, I personally dislike both MM-DD-YYYY and DD-MM-YYYY. Mon DD, YYYY is fine. YYYY-MM-DD (ISO8601) is fine (and to be preferred when naming files or in any other context where you'll be seeing lots of dates at once).
Side note: Military format 12MAR24 seems both concise and unbiguous but most people understandably find that unusual (just like ISO dates)
But the convenience of ISO 8601 for electronic form is compelling, and it has slipped into my writing as well.
Also, tell me: what date is 10SKÁ11? Or 01DU02?
Furthermore, a lexicographic sort will do the wrong thing.
Better stick with ISO 8601.
Of course it lacks many advantages of ISO8601 like sorting correctly in alphabetical sorting or working across languages, but it's a huge step up from 3/12/24.