Yes, MM DD YY only makes sense when you're speaking.
In written language it should always follow the order of smallest to largest, meaning day, month, and then year. Imo.
Though I personally try to use YYYY-MM-DD as much as possible in day to day life, if not applicable I use DD MM YYYY. YYYY-MM-DD of course doesn't follow the order of smallest to largest, instead following the opposite order, though at least it has an order.