In Australia, everyone pays an extra 1% or more (if your income is high) for a program that we call Medicare. It is different from the US medicare. The money for this scheme goes into subsidizing medication and GP visits (you pay to see the doctor and you get up to 80% back) and a few other medical things.
Private health insurance is an option that covers other things that the government will not. It allows for elective surgery and necessary surgery to be done quicker than in the public health system.
We also got braces with our private health insurance for half the regular price.
So basically we have a national and a private system each taking care of various things. It is not the most ideal system but it seems to work.
As for the microchips. They are a bit scary. However, if a patient goes to several GPs at different clinics, information is hard to get due to the lack of information transfer and such. This chip might help solve this. It also may be useful in an emergency situation when a person is unconscious.