During (at the beginning) of GFC all Australian banks were insolvent. They borrowed short term and lent long term, what is called 'classic miss-match' of terms, the international money markets froze, our banks were unable to rollover their short term due debt securities, the government stepped in (and the RBA), the rest is history.
The RBA's only tool is setting the interest rates, they do that via the banks. As such - i consider the RBA (and APRA) no more than a tool of government to influence private/public investment choices.
Anyway, you don't have to worry about the 'Big Four', they are perceived 'safe' by international markets. (see chart -5 year CDS spreads on Australia's 'Big Four' banks - once again retreating, which indicates that there are not yet any funding problems on the horizon (the big four get most of their wholesale funding from overseas sources).
All perceptions about bank safety could change very quickly if the housing bubble would burst. The RBA could never stop it, just as the FED couldn't.
In regards to banks source of funds - there are 3 major sources, all with 3 have different cost structures. I may write about it more, but you are not wrong - the banks have increased their profit margins while most of the Australian industry sectors are still suffering.
Sorry, haven't checked TD rates in France, however there is nothing to stop Europeans (Japanese) to borrow home and invest in Australia to compete with you and i.
