Comic strip of a ghost and a person with the American flag pasted on the head. The ghost repeats "Boo!" in the first three panels without getting any reaction, but when it in the fourth panel says "kg, cm, km, °C" the American gets scared and screams "AHHHH!!!".
Lots of stuff is written differently, than it is spoken. In case of the date it is weird, not to go from biggest to smallest or vice versa. I guess you are used to it now, but for me it would be the same as putting seconds before minutes or inches before feet.
Depends on context, IMO did/mm/yyyy is the most natural when writing some text, but partial ISO yyyy-mm-dd is ideal for when naming files and directories, makes lexicographical ordering follow chronological order.