Australia has a dual system of private and public health coverage.

You get access to public health services but as with all public health services things take time. If you have private health insurance you get a faster access to specialists. Public health doesn't do stuff like dental or physiotherapy where private cover does.

In addition to what slazer said, in Australia once you earn over a certain amount you get hit with an extra tax if you don't take out private health. The conservative coalition brought that in a long time ago because their donor mates in private health asked them to ruin our public health care and this was their first step towards that.

I still have private cover as it seems like the least bad option even though it pisses me off. I guess that's the point.