So the first point was that depending on your files/archives and how you access it, year or month or day may be more relevant to the user, which is why I was saying it's dependent on the user, so I don't agree that a human centric solution is always going to say the year is less relevant.

And then if we are going to prioritize organizing the numbers in such a way as to save the eyes a millisecond of time, for standard usage month would be the orienting date since you need to make sure you are looking at today's month, and then day would be the next necessary date, and then you'd still need the year there, so you'd end up with Month Day Year. Putting Day first would be just as wrong as putting year first because it is irrelevant until you establish the month, it's too granular.