Interesting bit that I forgot to mention.
Turns out, the eligibility to sit the test is only confirmed after all the background checks are complete. Some are done by the processing centres and some (newly introduced) are done in Canberra (which can take time). Only after these return all clear, the candidate will be allowed to sit the test.
Furthermore, only after the test is passed successfully, immi processes the final onshore police check (AFP?) and the application can only get approved after it shows all clear. For some people, the results come back the same day, for some... we all know it can take a while.
The above were the answers to my questions from an immi officer about the processing timelines discrepancies between candidates. I didn't ask any questions about application buckets or anything like that.
In cases where a family sits the test together and not everyone gets the approval on the same day - my (somewhat random) theory is that the rarer your name is, the quicker you will get approval if your police history is clear. Because surely there's plenty of John Smiths with rich criminal history to check against before they make sure you're in the good books.
Just my 5 cents!