That goes back to the 80s when commercial stations in Australia found US morning shows a great and topical way to fill a few hours of overnight programming in the first few years of 24 hour broadcasting. Because of the time difference, we could get quality network news from the US at 1 or 2 AM. You're right, Seven were the first to do it. But they actually aired CNN originally. Later, in the early 90s, 10 got exclusive access to CNN and carried it midnight to dawn.
NBC Today aired for many years from about 1 AM on Seven. Despite airing in the graveyard shift, it gathered such a cult following that it was regularly sent up on our version of Saturday Night Live for years. The comedians' take on it was much the same as my first reaction on seeing it as a kid after living in England for some years. I had never seen news anchors do that much inane "happy chat". My dad was like "what the?!" but I loved it! It was just a whole other level of "anchor stardom". Yes, big name 'newsreaders' in England were paid big bucks and were household names, but there was a sense of formality and authority (that was never really repeated since). I loved the English anchors who were so professional and matter-of-fact (as you can see on my YouTube channel).
The big "handover" of the alarm clock between Jane Pauley and Deborah Norville perfectly illustrated this bizarre netherworld of "TV anchorland" that the rest of the world grew to emulate later (Recorded on Seven affiliate near Sydney.)
Another recorded on Seven.. (and damn.. Katie really fluffs that accent at the end!
The 'inanity' level was, in fact, exaggerated because we used to receive that part of the 'Today Show' produced for stations without local news at :25 past the hour - the 'co-op' - where the cast would chat.. and chat.. and chat about any old thing. Of course, none of us in Australia realised that it wasn't really intended to air widely.. it was only meant for Flintstick, Wyoming and other such one-horse towns. We thought it was an actual part of the show where they return from commercials and literally talk about themselves for an entire block!
Here's my 2 contributions to the co-op files.. again from Channel 7. You can see what I mean about the happy-chatting anchors that we were so unaccustomed to!