The point of having private health insurance in Australia is time. And expertise.
For example, in Thailand I had an inguinal hernia. Quite painful.
I flew back to Australia. In one weeks' time, I had an appointment with the surgeon. A week later, I was on the operating table. With one of the top surgeons in Melbourne.
In the public system, I might have waited 3 months for the initial appointment, and another 3 months for the operation. I would have got whatever surgeon the system decreed.
Emergency care is not the same, it doesn't make any difference if you are a public or private patient.
I do know a former work colleague who needed a hip replacement. He spent 18 months living on painkillers, heaven knows what that did to his kidneys and liver.
IMO retaining my private health insurance is one of my better life decisions.