In reality most healthy individuals want a limited amount of care, sick individuals want the least amount of care required to return them to health - and there are fundamental limits on the amount of care that can be provided to those who are beyond the help of current technology.
As such you would expect a finite level of demand from the economy as a whole if everyone was allowed as much healthcare as they desired. Any attempt at rationing care will both reduce efficiency, and constrain supply - driving up prices. The most market oriented system would leave supply unconstrained and provide universal and automatic coverage allowing more suppliers to enter the market until supply outstrips demand and "prices" naturally fall.