Lastly, I don't believe there is an existing national health care system in any country where that healthcare isn't rationed.
Any health care system has rationing to some degree. Since there's generally a limit on how much money is available you have to have some control on the amount of health care you provide. This is true even with private health care insurance, which are neck deep in regulations regarding what they will and will not pay for. But in general, the more government is involved the more rationing you have. Even a true free market fee for service system has rationing to the extent that unless you're super rich, there is a limit on what you can pay for.
One other point: there seems to be a lot of confusion on the difference between a government funded health care system and a government run health care system. In a government funded system the government pays for health care provided by private hospital and doctors using taxes and/or payments. These include Medicare and Medicaid in the US, and the Canadian system.
In a government run system the hospitals and doctors are government employees. Examples are the VA system and the UK system.
Most of the talk of reform in the US centers on government funded systems not government run systems.