So if you made an appointment for the 2nd of September you'd tell 'em "yeah let's meet on the 2nd" or "yeah let's meet on the 245th" you're gonna need the month somewhere.
Of course if it's the same month it wouldn't make a difference if you said "let's meet on the 10th" or "let's meet on the 10th of August" but if you're making appointments for different months which in everyday life or in a work environment is not unusual you can't just say "yeah the 2nd" and expect them to know which month. "Yeah you can expect delivery by the 4th".
Tl;Dr:
I didn't even say "it's the only way to say it when speaking" I said "only makes sense when you're speaking." because in written form MM DD YY is just shit for everyone except Americans, to the point where context sometimes is the only saving grace. Vice versa applies.