When you write down “07/01/1967” are you unaware that it is unclear whether you’re referring to July 1st or January 7th?
And despite the fact that you’re writing something down for the express purpose of communicating information, and you’re choosing to shorten it’s written format to save time and space, you’re ok with either
a) just leaving it ambiguous and communicating poorly
or
b) having to write extra words to give it context, taking up more space than just writing out “July 1st, 1967”?
1967/06/01 clearly communicates we’re starting with the year and going biggest to smallest time increments. There is no ambiguity as to which order it’s ever in, and it’s far shorter than the full written date.
At a fundamental user experience level, it is objectively nonsensical to choose the American date format when your goals are 1) clearly communicating a date and 2) doing it shorter than writing out the words.