It doesn't, I agree. What does make sense is yyyy/mm/dd. Because then you can nicely order your documents without having to rearrange the date thing. Not that it matters, of course. Just that it would make more sense to put the bigger numbers on the left just like we do with normal counting. But we totally don't have to.
In my diaries, which survive since 2006 iirc, i just write the year in the first entry of that year, and then only day number and month, until the year changes again

Offices likely just keep documents (or they used to back when they did not have by law to use computers for cataloguing) in huge dossiers, with the year or year+month written on the cover.