I'm assuming the rational behind drawing the distinction between the US and Aus systems is to somehow inform what the US should do, I don't think giving an already corrupted government system more power will help. It's very hard to uncorrupt things and because of that reason I think the US would benefit from a more laissez-faire system.
Additionally Australia has many advantages that the US does not and the US could not emulate Australia even if they wanted to. I don't know how long that'll last either - mathematically I would assume a country could not get rich and stay rich repeatedly selling houses to each other but it does seem to have lasted a very long time. I assume at some point the Aus government will run out of ways to prop up the housing market. The combination of negative gearing and all sorts of first home buyer grants is just insane.
The current system grew out of a more fully public system under a many years past Whitlam government, people like the universal health for all aspects and wanted additional private services in the mix. It's evolved from there, with government oversight directed towards keeping things accessable and fair.
The US appears to have "massive government regulation and dysfunctional state intervention" as the end result of a lot of fingers in the pie bending regulation toward "middlecare" providers that don't apply splints or save lives, just diddle about with insurance schemes. (Admittedly that's just an impression from afar).
> The US government helps make the dysfunction that private equity later exploits.
My feeling is the US government is largely an arm of private interests in many matters.
Health Care in Australia embraces public policy such as Food Regulation to ban and limit additives, parks and sports grounds to encourage exercise, limiting access to tobacco, and some interesting national level drug acquisition deals to keep pharmacy costs low.
These cause a flow on of less per capita input into the medical side; lower heart disease, less smoking related issues, etc.