I think there is a primordial need to believe in something greater than ourselves. Maybe it's simply an innate evolutionary design/trait that has allowed us / prevented us from screwing each other over. Potentially, it is simply an illusion we talk ourselves into.
However, it does seem too often that things just work out in a manner that is too predictable to simply be random chance. Then again, evolution would also explain some of the predictability.
I don't know that anyone can say with certainty that the concept of a "higher power" is false, we are learning to re-engineer life as I write this, not a great leap in "faith" to assume we'll someday be able to create "life". When we do, we would be the "higher power" who designed the new life and the systems in which they exist - could this not be our reality today?
RE: Australia shedding religion from their culture, "No Religion" is now primary belief.