I think that's too much thinking, I'm pretty sure it's simpler than that. North Americans say "December Twelfth" or "May Forth" or "March Fourteenth" rather than "The Fourteenth of March".

So they go "March -> 3", "Fourteenth -> 14", and you get "3/14" that you can read from left to right as "March Fourteenth". That's about it, I'm pretty sure.

And so long as everyone agrees which one comes first it's not ambiguous. Of course, everyone doesn't agree, and there are logical reasons to pick the others, but this one is simply in reading order.