The most intelligent way to write the date is year-month-day. You start with the big numbers first and then get more detailed at you read across. Just like with a regular numbers where you start with thousands first and then go to hundreds and tens and ones. But nobody would want to do that in real life because the year changes so slowly. It just gets in the way as you are trying to get to the point. The American way is a good compromise between making sense by having the big number come first but being easy to use in every day practice by getting the clumsy year out of the way.

Months change pretty slowly too... day first is most useful in most circumstances

Especially for sorting! That's how my photos are named when downloaded from my camera.