The New Zealand or Taiwan model works because you don't let the virus enter in the first place.
Also New Zealand and Australia are in Summer right now. Just 30 seconds of Australia sun radiation now will kill(inactivate) any virus on any surface. Temperature will dry the membrane of any COVID virus that remains on the shadow. People immune system is much stronger in Summer, and people go out, do not live that close together as in Winter.
Once you let it enter like the UK, Spain, Italy or US did, it is too late.
It took three months for the Spain going "from 1 to 0", and it was the biggest catastrophe for the economy and democracy itself in decades, because it takes time for the spread to halve. And it did not get a real 0 after all the pain. Spanish' Spring and Summer had probably the biggest effect after all.
It is not that catastrophic by the way. Once people get infected, they do not get infected away, and just protecting people over 65 years old with vaccine will stop most deads.
In fact just going for people over 80 years old have a significant effect on deads.
In the US, 15% of the population is over 65 years old and 9% already got the first dose. Next month most of them will be immune.