Germany is two-tier. Public health for the masses, private for those making over 80k or so and healthy.
The public system premiums are a % of income. The private is a flat cost, so as you make more become much more attractive (even costing less in many cases).
Doctors are sometimes private only or have separate private insurance waiting rooms. Hospitals have separate public and private rooms/beds, etc.
It's a two-tier system that works pretty well, at least in comparison to the US system.
My info is a few years dated, but is based on having been a patient in both US and German hospitals. From friends, I've heard the English system is similar in some respects to the German.
Amazingly to me, the German system was instituted under Otto von Bismark in the 1800s.
Aren't the public premiums only a % of income up to a certain cap? So it's not like super high income people would pay an outrageously huge amount to use the public system, they would just potentially pay somewhat more than they would if they got private insurance.
This ensures that the system works better than the US system, as the hospitals do not need to deal with having to treat uninsured patients who cannot pay. This is a major problem for the US healthcare system, and a critical threat to the solvency and continued operation of many hospitals, especially rural hospitals and clinics.
The insurance mandate is a principal component of the ACA. In the US you have to have health insurance or you pay a fine, and there are subsidies to help people pay for insurance. To further lower the number of uninsured in the US would involve increasing the penalties for not having insurance, paired with further expansion of subsidies or Medicaid. Honestly sounds like that area of the Swiss healthcare system is pretty similar to what the ACA provides.
Switzerland also regulates drug prices... and has much tighter governmental oversight over their insurance industries. But is also the most costly by percent GDP of european nations... still much much cheaper than the US though.
In a sense Germany works very similar to Obamacare. Private doctors, health insurances, mandatory insurance for everyone. The difference is that it's much more regulated and the insurances are non-profit as far I know.