YMD is logical, because it puts the most significant number on the left.
But both DMY and HMS are consistent in another way - the information is ordered from most to least important for every day access, from left to right.
A vast majority of dates on advertising, tickets, timetables etc actually leave off the year, unless it's ambiguous. Similarly, one might say something like 'on the 4th', which implies 'the 4th of this month' (or the 4th of next month, if applicable).
This is the reverse of HMS, where the most significant number (the hour) is most important, and seconds are basically ignored day to day.
MDY, on the other hand, should be taken out the back and shot (IMO).