All of economics boils down to the rational allocation of scarce and limited resources between the individual members of a system. In its most basic form, it is the study of human action / it is a decision science. In the case of the United States, for example (just chose the US arbitrarily), there are about 300,000,000 autonomous or semi-autonomous (e.g., children, dependents, crippled, etc.), rationally-acting, and inherently self-serving organisms (this is by biological design - some capacity for generosity and self-sacrifice exists by biological design as well, but it breaks down on the larger scale; it really only functions well when the individual members know each other well; e.g., living in a village), all seeking to survive and reproduce.
Given that there are basic necessities that enable life functions that each organism must acquire, how best to allocate these resources? In the case of a small village, individuals could meet up, discuss things, and cooperate with one another and come to some sensible agreement. Each member of society has a vested interest in his or her own personal survival, as well as the survival of his or her fellow villager. In this sense, central planning is made much simpler, and forced compliance may not be necessary since each villager knows one another and might be more inclined to cooperate (although forced compliance could be achieved through shaming, guilting, or even force if need be - every now and then someone might disagree).
As the size of the population increases, however, this simple village model becomes increasingly more complex until it, in fact, breaks down. It breaks down for two reasons: 1) Lack of information. 2) Lack of compliance.
Friedrich Hayek published his seminal work and his classic critique of socialist systems and planned / command economies in his work "The Road to Serfdom" (If you enjoyed Orwell's 1984, Serfdom will be nothing short of enlightening for you - like reading the screenplay or the behind the scene's look at 1984). Here is his fundamental premise: http://www.youtube.com/watch?v=CNbYdbf3EEc (He does not oppose socialism on the grounds of morality, but on the grounds of technical unfeasibility)
Going back to our discussion, the reason why market economics works is because instead of having one single entity trying to centrally plan and direct all of the human activity within society, there are literally 300,000,000 entities all coordinating with one another in real time via supply, demand, and the presence of price information, and information is the key here to all of economics. Price is a single, unified piece of information that lets each individual actor in the system instantly assess a good or service's relative value compared to every other good or service in the system at that point in time. It is sensitive to local and global supply and demand, and can change instantaneously to reflect scarcity, abundance, time preference, and other variables - it does this all in real time, synthesizing every other variable simultaneously (e.g., the price of a hamburger must take into account the price every single ingredient, every service that must be rendered in order to prepare, market, and deliver it, as well as other random factors such as time preference, time of day, season, etc.).
The second critical piece of information in an economic system is profit. Profit is not a dirty word. Profit is the signal that tells us that we should do something for someone whom we do not personally know. Profit, along with the presence of price, is what enables the rational allocation of resources in a sufficiently large system of autonomous, rationally-acting, self-serving organisms.
If we are to respect individual autonomy, then we must accept that no single economic system ought to force the compliance of all of its members through force (unless every member agrees. again, in the case of a village it might work, but as the population size increases, this gets hairier). If we could enforce compliance on a large scale, then we could make the economy incredibly efficient. Hayek and other classic, Austrian, free-market economists valued individual autonomy, as such if you want to maximize this variable, then you must minimize the central control variable in order to enable maximal efficiency of rational allocation. If you want maximal efficiency from a central-control standpoint, then you must minimize autonomy.
And yes, this argument does, in fact, apply to health care. "Health Care" is just an umbrella term. What it and any other "market" comes down to is the rendering of services and execution of tasks. Here are the real questions you have to ask yourself:
1. How big is my economic system?
2. How easy will it be to enforce compliance of societal members?
3. Is this just?
In general, markets work great when there is the presence of accurate price information, competition, and no externalities / distortion of normal market mechanisms through things like excessive subsidies, taxes, and regulations. More often than not, it's those companies that lobby hard to get bills passed that specifically favor them that fuck the whole thing up. The issue is corporatism, fascism, and crony capitalism - not normal market mechanisms in and of themselves. The politicians (especially the Fed) are just as much to blame as the companies that benefit from using force or fraud to achieve their ends.