The count was off because a number of the cities weren’t marked as being nested. I’ve fixed that nesting up as best I can in Victoria, but there are some that can’t be marked as nested.
In an effort to deepen my understanding of the conversation 
so far (and in many cases remind myself), I reviewed these levels.
- Relation: Melbourne (2383266) | OpenStreetMap (level 9)
- Relation: City of Melbourne (2404870) | OpenStreetMap (level 6)
- Relation: Melbourne (4246124) | OpenStreetMap (level 7)
Each of those pages includes a link to its Wikipedia page. Those pages describe the level 9 place as a central business district (CBD) and the level 6 place as a local government area. That level 7 entry is the metropolitan area.
That also lines up with Sydney (with some missing Wikipedia links)
- Relation: Sydney (5729534) | OpenStreetMap (level 9)
- Relation: Council of the City of Sydney (1251066) | OpenStreetMap (level 6)
- Relation: Sydney (5750005) | OpenStreetMap (level 7)
Outside of Sydney/Melbourne, it does look like admin level 9 does a decent job of matching “city”. Shire of East Gippsland - Wikipedia and Golden Plains Shire - Wikipedia are admin level 6, and list out several towns which end up being level 9 in OSM, as examples.
Once you get to Melbourne etc the two levels are not compatible. I can’t cleanly nest the 9 into the 6 and get full coverage, and I can’t nest 9 into 7 for the same reason.
As a person who is just about as far away as you can get from Australia… the municipalities (level 7) seem much too large and the conversation seems to be down to choosing 6 or 9. LGAs (level 6) seem decently useful in urban areas, and then expand out quite a bit in the more rural areas.
It might be time to send a very short survey to anyone who has completed a street in these places to get some local opinions…
(I’m having similar difficulty with places in England)