We have a govt run system is Oz and though there are long waits for non-urgent surgery out system works really well.
We have the option of having private insurance, which I have because I want to choose my doctor or use the doctor I am referred to by my GP.
Our system pays for 80% of medications for low income earners, 95% for pensioners & unemployed and has a safety net which means once a pensioner or unemloyed person has spent $300 on meds the meds are free for the rest of the calender year. This year we had spent $300 by March.
What I object to in our system is the administrators of the public hospitals running the hospitals like a business and are stopping people from getting treatments they need and closing hospital beds so that they have a surplus at the tax year end and receive a bonus from their employers.
The system does work, and it is a matter of not actually expecting private cover treatment from a public system. The Public hospital system saved my life several times and I am very grateful to it. And I am very grateful to live in a country that actually looks after its people. All countries should do that.
Medications here are charged at the same subsidised rate as it is in the private sector. And the treatment is not decided by the govt, but by the treating doctor