It makes me sad to read something like this about one of my favorite NZ places. Though I'd like to think it's only this way in peak-season (summer).
https://www.stuff.co.nz/timaru-heral...-quite-a-stink

Wow. I've always admired how NZ does such a stellar job of providing free, clean public loos...are people just complete pigs or is NZ seriously overwhelmed with tourists? I suspect a bit of both.

We learned first hand that Iceland has a similar issue - but they have a severe shortage of public facilities - especially in popular tourist spots. IMO Iceland Air and WOW play a big part as they're the ones pushing the free stopovers that have introduced Iceland to the masses. I think they should impose a tax on those two airlines - or on ticket sales - and invest the money in public facilities to accommodate all the tourists they're bringing in.

A photo I took in Iceland:

https://www.flickr.com/photos/melnq8...7685764997076/

And a few articles discussing this problem:

Tourist Defecation Problem Resurfaces | Iceland Review

https://icelandmonitor.mbl.is/news/n...oops_next_to_/

You're right, the problem is both. It does appear that Iceland and NZ have similar tourism-based problems. Lord of the Rings and The Hobbit boosted tourist numbers for NZ. I've read Game of Thrones did the same for Iceland. I've not seen GoT, but I know it is wildly popular. An airline tax seems reasonable, but I don't think Iceland residents should have to pay it.

Human faeces and toilet paper have become problems throughout New Zealand, mostly at freedom camping sites and at popular tourist spots, but almost anywhere really, including private property, beaches and school grounds. In Tarras, 10 and 12 year olds complained to their town council of tourists pooping on their school grounds.
https://www.stuff.co.nz/national/edu...-tarras-pupils
Akaroa has demanded the Christchurch City Council for a "poo patrol" and will likely ban freedom camping from their town:
https://www.stuff.co.nz/business/100...reedom-campers
Scarcely a week goes by when I don't come across articles like the above. But new public toilets cost a lot. The new public loo at Dunedin's Baldwin Street cost $177,300. I'm all for a NZ tourist tax, something modest like $20 to $25 to cover public loos and their maintenance, emergency helicopters and ambulances and LandSAR (Search and Rescue). Any leftover funds could go to DOC. It would really help.

The French Embassy of New Zealand warned French tourists to have "good manners" after several egregious incidents. A Frenchwoman freedom camper was filmed defecating on a Dunedin street 100 metres from a perfectly functioning public loo. Another French tourist caused a grass fire at Lake Pukaki after he set his used toilet paper alight. Two French tourists were filmed urinating from a moving vehicle; they found it amusing.
French woman caught defecating in a New Zealand street | Daily Mail Online
https://www.stuff.co.nz/national/770...olice-warnings
https://www.stuff.co.nz/travel/trave...ar-Lake-Pukaki
French Embassy warns tourists against open defecation | Newshub

Very, very sad. One of the many reasons we visit outside of the peak season is to avoid the crowds. I doubt building more facilities will help the problem. NZ already has more and better toilet facilities than anywhere else in the world I can think of. I think many people are complete pigs, how to deter that type of people from visiting is problematic. Maybe the NZ government is pursuing tourist revenues at all costs?

They could easily reduce flights into the country by reducing the number of landing slots, either across the board, or from certain countries (if they have any means of identifying the main perpetrators s by nationality). Maybe tax flights and invest the proceeds in covert poo wardens to police key areas and issue on the spot fines (big ones!)