The healthcare system in Australia is fundamentally broken & not fit for purpose. Massively under resourced & bled dry by medical practitioners. Read recently that GPs are leaving the NHS to work in Australia & are trebling their earnings & working less hours. Don't believe a word from the AMA about GPs being hard done by, make them all bulk billed.
Even the private insurance model is broken, take a out gold plated top level private health coverage & you still pay a significant gap. If you're healthy private medical coverage isn't worth it unless you're doing it to save paying the medicare surcharge, just self insure.
Health services are a fundamental human right that IMO should be free for all at the point of delivery. There should be profiteering within a public healthcare sector.
Have a private health system, no problem, but make it sustainable & have the premiums people pay actually cover 100% of the costs, bar an insurance excess & a flat contribution by the government. If you want to jump the queue for an operation or have a nice fancy hospital with nice meals then you have the option to go private for a one off procedure.