"less likely to die from drug overdoses. Older age groups are also less likely to die from chronic diseases such as circulatory problems and heart disease. Cancer mortality rates are lower in Australia than they are in all other Anglophone countries, except among American men aged over 65. And Australians are also less likely to die in road accidents than other countries"

So what does this have anything to do with healthcare system ( govt or free market) .

Looks like you conflated two unrelated things ?