I see the duality in this but I still think both are valid. When telling the time, there’s usually no point in including the seconds since they’ll have changed before you finish saying the whole thing anyway. In spoken word IMO it makes sense to go from more specific to less specific, and even not include extra parts sometimes (e. g. “today is the 3rd” when it’s expected to know the month and, well, year from context, or “it’s half past” to someone whom you’ve told the time a couple of minutes ago).
I see the duality in this but I still think both are valid. When telling the time, there’s usually no point in including the seconds since they’ll have changed before you finish saying the whole thing anyway. In spoken word IMO it makes sense to go from more specific to less specific, and even not include extra parts sometimes (e. g. “today is the 3rd” when it’s expected to know the month and, well, year from context, or “it’s half past” to someone whom you’ve told the time a couple of minutes ago).