The sane ordering outside iso8601 revolves around the most significant bit. When you ask for the time, 34 minutes is usually not significant in any matter in written contexts since you could be reading it more than an hour later. Hence hours are more significant than minutes (verbal can often be an exception, "20 minutes past" can be enough context if someone asks for the time). But the "time" part of datetime is always more significant than the "date" part. The year is least significant since that one changes the least, then comes month, and lastly year. In many contexts knowing it is 14th of September is enough. In chats it might even be enough to say "14th" if you're talking about a date in this very month. But due to the timespan between writing and reading, minutes more often than not is meaningless without hours, hence hours become more significant.

Of course HH:mm dd/mm/yyyy is inferior when it comes to computer parsing due to iso8601 being the easiest to sort. (And because of Americans it is the only format to cause no confusion). But it is going least significant first in the sense that you are presented with year first, something that is often redundant in human-to-human interaction (depending on context you might say year is more significant than time in the case of wanting to know when an article was released, but you know, there's always more exceptions than rules).

So to sum it up: Use whatever date time format you want as long as you use a format fit for the context it is used in. Unless you're saving it to a database/directory/etc. Then use iso8601 so I can easily sort it.