Last couple of days TVNZ complains I'm not in NZ when I first try to stream a program. Force Refresh in the browser fixes this, but there must be some odd CDN issues upstream.
I start the news from the beginning regularly by going to the show via On-Demand and they selecting play from start.
This thread (speaking as the OP :-) ) was specific to the TVOS app on Apple TV 4K which has never and still doesn't, support play from start. Every other platform seems to have this.
Like others, I'm resigned to starting from the live point and rewinding back. What I did find is that using my TV remote will allow 4 different rewind speeds where the ATV remote only seems to provide 1 (Slow) and requires holding down on the side of the remote the whole time.