I haven't read every single post, so I'm sure it has already been mentioned that the Australian system works pretty well. We pay a percentage of our income into the health system called Medicare. That percentage is slightly less if we also pay into a private scheme, but that's not mandatory.
We pay for prescriptions and doctors' appointments, and we get an automatic Medicare rebate depending upon the procedure or appointment. We can then get a further rebate if we have private insurance.
Those on a low income aren't charged. So, healthcare is free at the point of delivery for anyone who can't afford it.
This only applies to non-urgent conditions. You don't need any private health insurance for emergency care or cancer treatment, heart attacks, maternity, etc. That's free for everyone. Some people still prefer to use their insurance and go privately for everything, but that's their choice.
Some states have ambulance insurance too, which doesn't cost very much per annum. Otherwise, you can be charged for an ambulance if it isn't deemed to be urgent. But again, those on low incomes won't be charged.
We have all too much reason to know the ins-and-outs of a large part of the the Australian medical system. Honestly, the care one of our family members has received over the past few years has blown the care they received from the NHS out of the water. That includes mental health care, which was almost non-existent in the UK.