We could drop the level8 boundaries but are you sure that is really a good idea? New Zealand doesn’t see to have an awful lot of area features for the places. Looking at a few the boundaries, they seem to come out okayish and some of them even have the wikipedia/wikidata links to the community itself. So it might be good to just leave them in as the area for the respective communities. Doing address calculation only with the place nodes is always more prone to error.
That is a common misconception about Nominatim. It doesn’t return “addresses” as such, it returns what I like to call a “location descriptions”: a sorted list of useful reference points that help placing the result. The list intentionally prefers to err on the side of including too much. That’s because it has to work with messy OSM data on a world-wide base. (But it’s also because I find result lists of competing software that presents you a choice of ten undistigishuable “Newtown, New Zealand” not particularly useful. )
Government structures tend to wary widely over the world, which makes it very difficult to find a unified structure. If you look at what other database have done, you’ll find that they generally start with a structure that fits their country of origin and a couple of close-by countries (and usually only fits well for urban areas) and when they expand to other countries (or in the country-side), they just bend the local structure until it fits into what they already have.
OSM goes a different way here. We let the the local communities optimise for their local situation and expect the data user to normalise on their side. The advantage is that OSM has a lot more nuances than any other database. The disadvantage is that the normalisation can go wrong at times.
The other aspect to take into account here is that the administrative structure of a country is not necessarily the same as the human perception of the structure of the country. And that again may be different from how the postal service partitions the country in order to create official addresses. In OSM, boundary=administrative correctly reflects the governmental idea of country structure, which doesn’t make it always useful for the second. We do have place=* tags for the human perception but given the rather fuzzy nature of defining human perception, the data in OSM is still inconsistent. For addresses, we have yet another schema, the addr:* tags. Sadly, that goes only on address points and isn’t applicable for non-addressable features.
In short, OSM data isn’t really meant to be ready for consumption. Nominatim is one software that is supposed to do much of the normalisation. In fact, it has a geocodejson output format, which returns neatly sorted address categories state, city, suburb, street, etc. So pretty much doing what you ask.