"But why was George M Cohan born on the 4th of July (British style) and not July the 4th?"

That's one of the few dates that just sounds better said that way. "The Twenty-seventh of October" would be a bigger mouthful. We have a tune called "The 8th of January" also, but when you ask someone when they were born, they are 'more' likely over here to say "January", and if asked for the date, it's January the eighth.... so, we write 01/08/1953 or whatever. This way, the leading numbers can be only 1 of 12 and serves to clarify the basic time period immediately, then the specific date follows.

Can one adapt to looking at the middle term to determine the month? Of course. Because of the internet, I have learned to translate in my head when I see what looks like a month beyond 12.

I also have a wonderful calendar program called Calendar Magic which asks for data entry in the m/d/y format, even though I thought the author was in the UK (trying to check on that)