Unlike the US, which had lots of people
dying every day and so chose Emergency Authorization to get any working vaccine ASAP, New Zealand already had eliminated COVID-19 in their general population, so they did the full (albeit expedited, it's not as though there wasn't impatience) medicines authorization process for the Pfizer vaccine they're using.
They've now put well over a million jabs in arms (New Zealand's population is about 5 million) and are starting their "big" population wide rollout at the end of July. There is no sign of any significant problems.
The very rapid success of the trial programmes is actually because we did such an abysmal job stopping the pandemic. Trials work by comparing people who got the test jab against people who got a placebo. For many diseases it might take several years for enough trial participants to get infected so that you learn anything. For COVID-19 it took only a few months for strong signals to emerge, because, (outside of New Zealand and to some extent a handful of other countries that had control) the virus was everywhere, so very quickly your placebo group began to get infected and sick.
HN deals more with technology. Imagine your project takes six hours to compile. You have ten hypotheses for the cause of an important bug. Will you fix it this week? Probably not right, that's sixty hours just for compiling -- maybe you can leave it overnight and manage two tests per day? But best not to chance it. So you tell management you hope to have a fix "the week after next". Sorry, that's the best you can do.
Now, imagine a new compiler version speeds up builds, and they only take 15 minutes. You can try all ten hypotheses in a morning, get a fix reviewed, go to production and it'll be done by Friday close of business no problem.
Management are suspicious. How can the new compiler make such a radical difference? Surely you've cut some corners, you'd better go back and test it "properly" this time.
In this analogy lay people are suspicious management and the vaccine manufacturers are the developer. Also being completely useless at preventing a predictable respiratory pandemic is somehow a new compiler version. That part of the analogy doesn't work very well. Sorry.