Which largely exist because American health costs for an injury are life destroying, so few people can just eat the hospital bill.

I mean, not really. Plenty of people get sued in Canada for personal injury (my friend specializes in it) and they have universal healthcare.

I don't know of any country that has a social safety net that 100% reimburses you for a life-altering injury where you can no longer work. Sure you'll get a disability pension, public healthcare and maybe a bit more, but it's usually "barely enough to live on" support.

If you're a doctor making $200,000 per year and you can't work again, suing is usually the only way to recoup things like lost-wages.

I think the point is in NZ there is basically no possibility to sue for the outcomes of a personal injury. The doctor will have to live a more modest life. Period.

In NZ people can still sue over business contracts and participate in legal cases against the government culminating in legislation being ruled unconstitutional, like other Anglo, common-law countries.

That's fair, I meant cases where the hospital bill is more life altering than the injury. An ambulance ride and some stitches is going to absorb several years savings for a lot of people.

ACC in NZ effectively did away with personal injury lawsuits, before that some people would not drive friends in their car in case they had an accident and ruin a friendship

Think it's probably more because unlike other Anglo jurisdictions, American lawyers can take matters on contingency, whereas at best UK/AUS/NZ lawyers can take them with conditional costs that significantly limit upside to the lawyer. This is also why the UK/AUS have such well developed litigation funding industries compared to the USA.

Isn't it also because the US has punitive damages that are awarded to the person suing, providing for an opportunity for a payout far greater than the compensation for the damages alone?

It exists also because legal system is setup that way. For Example I Europe there is tendency to expect more detailed regulation to decide where lines are. In USA you get more general law and then people are supposed to fight it in court. Courts then decide details by cases.

It is rather bug difference.

Also, insurance companies when they settle claims, they force you to formally sue the other person or they sue each other. Most of these are routine formalities. Again, system setup in a way to generate suits.