For sure, private health insurers exist and in a big way. In Australia for instance, there's still privately owned hospitals which do offer a more "premium" lev

For sure, private health insurers exist and in a big way. In Australia for instance, there's still privately owned hospitals which do offer a more "premium" level of service - i.e. better rooms, less surgical waiting times, ammenities, often where specialists have their offices, etc. Health insurance gives the option to use these hospitals and the insurer covers the majority of the costs. There's sometimes a 'gap' cost to pay. The thing is, it's not like you might die in the public side of things and live in the private side - you'll get the same kind of primary care. But health insurance becomes a premium service for those who want it. I'm sure there's a lot more to the story as well, but it's one of those things that I'm not an especially full bottle on.