Going day to day, dd/mm/yyyy works, but for archival purposes and looking up stuff in the past, mm/dd/yyyy works better, imo. Like when you need to go through a physical file cabinet, or an electronic database.
Or you're the type of person who's zoned out all the time and don't even know what month it is until you look at a clock or calendar.
Except it doesn't sort well in any fashion and it requires two different types of contexts to interpret. It's easier to screw up the order of a month by name than it is to screw up the order of a number. Not saying we should play to least common denominator, but we should be making it as easy as possible. I'd prefer sorting speed over needing to learn how to interpret the date correctly if every single date is stored the same way.
I just dont see why the hell you would switch? dd/mm works fibe in all situations and has some advantages sometimes, while mm/dd is fine sometimes, but generally worse or equal.