Australia has a hybrid public/private system. You can rely on the public system for pretty much everything, but only catastrophic medical services are well-funded (and even then ...). Otherwise you will need to get used to waiting in a queue.

Private health insurance then allows you to get the frills and to do so without waiting.

If you have private cover and need surgery to treat a non life-threatening issue, then you can usually get it done almost immediately. If you don't have private cover, you may be waiting for years.

Still, in US terms, our private cover is very cheap. I'm a single, non-smoking, exercising male, 30 years old. I pay about $1200 a year with a $500 gap. But I also pay $20,000 in taxes, a goodly portion of which make their way into the public health system (and far too much of which goes into middle class welfare, but that's by the by).