Britain did not send convicts to Aotearoa New Zealand because planners envisioned it as a respectable settlement for free citizens, and Australia already served as the designated penal also early Aotearoa New Zealand lacked the secure infrastructure to manage them.
The Brits sent their religious nut jobs to the 13 rebellious North American colonies who decided they didn’t want to play nice and seek a diplomatic solution to their trouble - they had to resort to violence (still runs in your veins a couple of hundred years later).
Convicts stopped going to America because the American Revolutionary War (1775–1783) made it impossible for Britain to keep sending prisoners there. When the American colonies won their independence, they closed their ports to British convict ships. Britain then had to look for a new place to send its prisoners, which led to the creation of penal colonies in Australia.
So the Brits needed somewhere to send their prisoners to. They chose 5 of the 6 Australian colonies. (Not South Australia) It’s a long way from the UK to Australia (which is a long way from any western country - which was the point of it all).
