Rationing is necessary in any arrangement where the customer and the provider of a product or service do not engage in a direct business transaction. In other words, the basic principles of economics do not apply when the customer deals with the provider but has a third party pay the bill. This is true regardless of whether the third party is a government or a private company.
That said, I understand what sounds like your predilection for a market driven system. However, having health care be strictly fee for service, in a standard market driven manner, is problematic because modern care involves so many different people and the need for a substantial infrastructure.