Is it "government rationing of food" if you can't buy cigarettes with food stamps?
The answer is no. What makes health care different is the current system of price controls imposed by, wait for it, Ronald Reagan.
Just before I became the health economist with Reagan's Council of Economic Advisers, the final steps were being taken to implement DRGs for paying hospitals under Medicare. DRG stands for Diagnosis Related Groups. The idea was to get out of cost-based reimbursement, which gave an incentive to have high costs, and replace it with a system of prices. That made sense. But what made it a system of price controls was that the government, along with DRGs, made it illegal for hospitals to charge even a penny more than the price the government came up with.
Then, a year or two after I left the Council, the Reagan administration took the next step of imposing price controls on doctors under Medicare. Doctors were no longer allowed to do what was variously called "extra bill" or "balance bill." They couldn't charge even a penny more than Medicare paid. That's what made it a system of price controls. Moreover, under later regulations, if a doctor takes even one Medicare patient, then he has to charge Medicare rates to all his Medicare patients even if those patients would rather ensure access by paying the whole bill (Medicare plus a doctor's additional charge) out of their own pocket. It is this system of price controls that is causing many doctors to take no Medicare patients.
Incidentally, the system of price controls for doctors was designed by William Hsiao, a Harvard economist, and explicitly based on the labor theory of value.
So Byran's and Robin Hanson's proposal is a good one--as long as it is accompanied by removal of price controls.