I mean, I spent a month traveling there, and had no problems using public restrooms on a regular basis. If I'm traveling here (mostly West Coast US) I have to make multiple stops before I find a clean restroom.
It could be that NZ relies a lot more on tourism, so people try harder to keep things nice. But hey, hope you enjoyed my anecdotal story.
It occurred to me (and people I know) more than once that I did flush, multiple times, and that the damn toilet just refused to suck up everything I put in there. And for some reason this was always in public bathrooms, across Western Europe. Hypothesis is that due to being used a lot and possibly not cleaned in the correct way there's to much deposit of bicarbonates limiting water flow and the force/pressure of the water being flushed isn't high enough to flush everything in there. Not much an automatic toilet could do about that btw.
I use public restrooms once ever two days (sometimes even more) and I very rarely see that. Maybe people in your part of the world are less educated when it comes to using public toilets, or the janitors are not doing their jobs properly (if it matters I live in an Eastern-European capital city).
As for the automatic toilets, I hate them. I only had the displeasure of using them once or twice, and let me tell you, to have that flush of water invade your lower exposed parts all of the sudden while you're doing your toilet-related stuff is not at all nice, quite the contrary. Those toilets are the work of the devil.