To me it makes most sense to either go from the biggest to smallest or smallest to biggest. In Japan it's 2022.04.13 and it makes much more sense.
I think that when discussing something that happens soon it's best to say dd/mm/yy, for example, if you have a meeting soon, it's best to think days first because the appointment will be within days not years or months. It's more often "Is the meeting on Wednesday or Thursday?" or "On 24th or 14th?" instead of "Is the meeting in 2002 or 2003?" or "Is the meeting in January or March?". But when you, for example, have a huge list of things happening between 1888-2222 it's best to list them by yy/mm/dd. For example, if you want to find a specific Pokemon anime episode, it's nicer to search for it if the episodes are listed year first than day first.
I never see any reason to list month first and when you see something like "Best before 12/05" and have to think whether it means 12th May or 5th December it is just ridiculous.