Americans generally want their health care system to do three things: (1) provide needed care to all people, regardless of income; (2) maintain our freedom to pick doctors and their freedom to recommend the best care for us; and (3) control costs. The trouble is that these laudable goals aren't compatible. We can have any two of them, but not all three. Everyone can get care with complete choice -- but costs will explode, because patients and doctors have no reason to control them. We can control costs but only by denying care or limiting choices.
In my forthcoming book on health care policy, I say almost exactly the same thing. Only it takes me a whole chapter to say it. The chapter is called "No perfect health care system."
However, I think that the objective of making care available to people regardless of income is not an impossible challenge--getting people to take responsibility for obtaining preventive care is more of a battle. What I think is the objective that really makes health care difficult is the objective of keeping people insulated from health care costs by offering "insurance" that is really a pre-paid health plan.
I call the three incompatible objectives Affordability (meaning overall health care costs--Samuelson's number 3), Accessibility (the same as Samuelson's number 2), and Insulation.