Well, here's the thing though, how can such a health care system be run, without resorting to something that might resemble a Socialist style program, without enough profit to run efficiently run healthcare?
We've covered this in another thread, but the short answer is that the system can be run as a monopsony, where private doctors provide care and are paid by a single government-run insurer funded by contributions from everybody.
How can you keep costs down without stepping on people's rights as well?
Monopsony bargaining power, and the refusal to pay for procedures that aren't necessary or effective.