Swiss healthcare is regarded as decent but far too expensive for what it is compared to the single payer systems in all its neighbors.
Paying for healthcare isn't the place you worry about inefficiencies and waste. It's going to get paid for, and the possible efficiencies of pushing paper around are dwarfed by the cost of actually delivering medical care. So what you actually care about is delivery of health care. Italy does this really well. They have public hospitals and clinics and private ones, too. If you go to a public one, you're covered. If you go to a private one, the government pays the same to the clinic that it would pay to the public clinic. So the public system serves as a reference that the private system has to match in efficiency, performance, and price.
There is no medical or macroeconomic justification for private insurance companies. It's historical accident perpetuated by monied interests.
I always go for a high deductible (and lower monthly fee) for example.
Edit:
(1) Costs for individual: It does cost me around 80 euros, my deductible is 800 euros (maximum allowed) and I'm 100% covered for medical costs at the physician and at the hospital.
(2) Costs for government: 11.9% of GDP.