Lead Balloon, I don't claim to have the silver bullet answer to the GA woes in Australia. All I'm trying to do is point out dissimilarities between this country and the US that would explain why point-to-point comparisons, e.g. hours flown per capita, may not be relevant without considering geography, urbanisation, and ..., and ... and so on. But in short, yes, you reached 25% with (wrong inaccurate numbers) while I 23% with more factual ones. The fact remains, Australians, on average, fly less per year in small aircraft than their US counterparts.
I conjecture that Aussie urbanisation is an important underlying factor and I think Vag277 rightly points out that other means of transportation have gradually become more reliable, definitely cheaper and, perhaps, have just become more convenient (that's where the over regulated legal framework might be partly to blame) to use on a regular basis. At the end of the day, that's really just that: unless you have an IR, taking the plane to go from A to B reliably (= be at B by time T on day D) is nothing but a hit and miss which will at best save you a couple of hours of commute but will come at the expense of extensive planning and money.
I'm too young to make any meaningful comparison between today's world with what it was like 30 years ago but I know this: the current trend is, sadly, for younger generations to leave rural areas and congregate in larger urban centres. I'm however old enough to notice that generations junior to mine seem more interested in virtual things (instagram, snapchat and the likes – I'm really no expert) and smashed avos and lattes than in actual stuff. Which is also a byproduct of this: in the last 25 years, the advent and adoption of the Internet has transformed the way we do business and boosted the economy.
In any case, if GA is to thrive here again, there will need to be an operational requirement (beyond that of flight training) that makes travelling by private aeroplane more worthwhile than RPT or road. That's obviously not going to be with a sudden surge in people getting their PPL but perhaps tapping into yet unknown needs. One example that comes to mind is that of a doctor (a cardiologist) who sees patients in rural areas one week a month. She figured that getting healthcare on par with Melbourne was simply out of reach for a lot of people in rural Victoria so she teamed up with a friend with a CPL who flies her to remote places with a small hospital and landing strip long enough to accommodate an SR22. The lucky bit here is that neither of them thought of it as a joint venture until they came to the idea somewhat by accident. I would expect that practitioners in other areas could benefit from GA in this way. The hard part is to raise awareness.