Least specific -> most specific is generally better in spoken language as the first part spoken is the part the listener begins interpreting.
Like if I ask if you’re free on “the 15th of March” vs “March 15”, the first example is slightly jarring for your brain to interpret because at first it hears “15th” and starts processing all the 15ths it’s aware of, then “March” to finally clarify which month the 15th is referencing.
The only thing practical about DD.MM.YY is that it is easier for the speaker because they can drop the implied information, or continue to add it as they develop the sentence.
“Are you free on the 15th” [oh shit, that’s probably confusing, I meant a few months from now] “of July” [oh shit, I actually mean next summer not this one] “next year (or 2025)”.
So the format is really a question of who is more important in spoken language: the speaker or the listener? And I firmly believe the listener is more important, because the entire point of communication is to take the idea you’ve formulated into your head, and accurately describe that idea in a way that recreates that same idea in the listener’s head. Making it easier for the speaker to make a sentence is pointless if the sentence itself is confusing to the listener. That’s literally a failure to communicate.