Noah Smith, writing for Bloomberg, recommend the “hybrid” health care system of Japan. Not fully single payer, nor fully private, the Japanese system manages to deliver unrationed high-quality health care at a fraction of the US costs, whether in terms of GDP or per capita and get excellent outcomes even though their population is older than the US population.
I spent significant time on the Japanese system. There is no network, or rather every single health care provider is in the “network.” Patients freely choose their own providers. The Japanese system emphasizes preventative care, and such care is often free. A 4% tax, subject to a ceiling, replaces the insurance premium. In general, the government pays 70% of the much lower cost of services and the patient is responsible for the remaining 30%. There are exceptions and special consideration for lower income people. Noah Smith writes,
The remaining 30 percent is covered by private health insurance -- either employer-sponsored or privately purchased. Spending on private health insurance to cover the 30 percent co-pay is partially tax-deductible.
In my experience many, maybe most Japanese find the 30% so affordable that they simply pay it out of pocket and do not bother with supplemental health insurance. In any case, I never saw a person not pay in cash at time of service.
If you do your own research, you will come across articles like this one claiming that the Japanese system is “buckling,” but then you find out the article is based on “informal” surveys of self-selected participants who often are not even Japanese, long on opinion and short on facts. There have been some problems with overuse, like clogging up the waiting rooms of clinics for every runny nose. The Japanese government has been encouraging providers to take a more active “triage” or gatekeeping role to cut-down on overuse. There is really no need to go to the clinic just to pick up cold medicine, and indeed, patients who present with a common cold will get no more than about five minutes of the doctors time, just long enough to write the prescription. Generally speaking, Japanese citizenry are well-satisfied with their health care system.