Even the healthcare professionals can't estimate the price of care before providing it, because it depends on the outcome of things like surgery and reaction to treatments which cannot be predicted. So there's no way to tell the patient beforehand that their care will cost x amount. In addition to this the customer often doesn't know what they want and has no basis for making an informed choice before seeing a doctor. This is fundamentally different than (for example) selling products in a supermarket where costs are known up front, shops can vary prices and quality, and people can shop around. So the benefits of patient choice of hospital and treatment etc are questionable.
Other countries spend far less using a single-payer system with comparable or better outcomes than the US according to the statistics on life expectancy and expenditure per capita on healthcare, so IMHO the US should have more and better regulation of the healthcare market, not less. Cutting out the insurance companies completely would be a good start, as at present they run a racket extracting billions from the US tax payer for questionable results.