I think it has something to do with differences in how Australian banks and EU/JP banks finance themselves.
Probably you need someone who is an expert in Australian and European banking structure to explain it properly. I'll attempt an overview:
Basically Australian banks have mostly AUD assets, when they issue USD bonds most of the USD proceeds are not really needed and can be swapped into AUD. EU banks have EUR assets but also substantial USD assets (eg. a loan in USD by a French bank to a company in East Asia). To fund these USD assets they rely in part on USD bond issues, supplemented by currency swaps in the opposite direction i.e. EUR raised locally are swapped into USD. This makes the cross-currency basis negative.
As you know, a negative basis means it is expensive to obtain USD by going through a cross currency swap (in terms of basic economics, too many people are trying to do this, as compared to people who want to go in the other direction, so it becomes expensive).
Of course that still leaves the question why the European banks have chosen to adopt this imbalanced asset/liability structure which leaves them needing USD funding while the Australians have the opposite policy of ample USD funding. I'll be happy if a real expert can correct me and take the answer further. (For ex. about Japanese banking and finance I know very little). Most of the real experts are at central banks and the BIS.