Indeed. MM/DD/YY is used informally and for datapoints (e.g. the Date field when you sign a form), but any time you are writing formally (e.g. a letter) you use Month DD, YYYY.

It's almost like MM/DD/YY is the abbreviation of "Month DD, YYYY"

XX/XX/YY is a terrible format and I wish people would stop using it.

01/02/03 can be January 2nd or February 1st, and often there's not enough context to determine which was meant.

Actually it can be February 3rd. I've seen YY/MM/DD format in use. But yeah it's horrible.