How often have the QF8 747/A380 flights had to divert to random South Pacific islands since they started the DFW flights?
Diversions to Nadi, Noumea, and NZ have happened. For the flights with Sydney or Melbourne as a destination, dropping short to either Sydney or Brisbane has happened far more often. Probably easier in a 787 rather than an actual big aircraft.
When QF8 was operated by the 747 it was scheduled as DFW-BNE-SYD, when it was an A380 there may have been the rare diversion to NAN or BNE but with the 789 I don't recall it coming to BNE. MEL-DFW and PER-LHR are both longer than AKL-JFK.
MEL-DFW has tailwinds, and will rarely be an issue. You're also not in the nastier parts of the US with regard to ATC either. PTH-LHR is relatively free of ATC constraints for most of the journey, plus there are plenty of options within Europe. Going the other way is again tailwinds.
One issue with jfk-akl in that direction is delays at jfk can be lengthy (moreover than flights from mel, per, akl, etc). I'm sure a number of us have had 60+ min taxis out to runway at jfk.
It's not just on the ground that ATC will be an issue. The amount of en-route holding that you can get, going to JFK is astounding, and you simply can't plan for it. The first time I flew there, I put on an hour of extra fuel, and burnt that, and all of the variable reserve as well. The second time, I put on two hours, and burnt all of that too. The third time, no holding or delays, and burnt none of it. Delays on the ground can be the stuff of legend. Being number 80 in the queue is not unheard of. And engines on the ground are going through about 500 kgs of fuel per engine per hour.
Looking at a pretty current flight plan out of Dallas to Sydney, the aircraft has just on 1,000 kgs of margin between the planned loading, and the maximum, and there's nothing in the way of holding/weather planned at the Sydney end. It can certainly be done, but you're into the length of a bit of string argument, where anything has a trade off.