Our healthcare is a socialist type system, but it is one I agree with, although I am generally more for freedom and less government and business....
You can have money, and then go broke, and you will not be tossed out down here.
It does somewhat depend on where you live too, in more affluent suburbs, you will find less doctors (GP) that will accept the govt payment, in blue collar areas, there is healthcare for those that need it.
I wont cite my personal experience, but, I will say, there is little point to paying for own cover, that is how good the public system is, and many doctors are still with the basic conscience that healthcare is something that should be provided without prejudice, but there is some slimy buggers who are all about business and wont treat those who do not have cash too splash, they are the minority though.
The mindset is that without this type of cover, it can cost more too when people get to a stage that they must be cared for, they are not productive, and cost the tax payer, people are not allowed to die on the streets here as a general gist of the system. You cant get your fake boobs, fake pearly whites, or whatever on the public teat though, only serious, basic, health needs.