Dragon,
Actually government can make a profit, in the sense that it sometimes has a surplus. What separates government from other corporations is the means which is acquires its revenue. Most corporations gain money for the direct exchange of goods and services for money. Government provides services, and would not exist if it did not provide them, but is able to raise revenue through taxes. So people are paying and receiving these services without necessarily their consent, as a result of the coercive power of government.
Though you are right (assuming I took you correctly), that Republican forms of government do not distribute a surplus to shareholders (except in the case of corruption), this fact is irrelevant because it does not disqualify governments from being corporations. And moreover, there are governments that do distribute the surplus to the shareholders. So with this line of reasoning, you would have to say that some governments are corporations and others aren't.
But whether they are corporations also does not disqualify governments from having a market-based description for why they exist.
We can then analyze the success of governments by how well they are able to service for the taxes they receive. A very inefficient government is likely to be overthrown, while one that is more efficient will be able to continue. We find many examples in history that support this model. Central planning, for example, is by its nature very inefficient compared to capitalism. These central planning regimes also were inefficient, with long bread lines etc, and unable to deliver their expansive range of services efficiently came to ruin in favor of ones that could.
With this line of reasoning, I believe that a government that provides a narrow range of services is generally better, because it would be more efficient. By government minimizing the number of markets it services, overall market efficiency tends to be improved.
The question here is, I suppose, is it more efficient for government to service health care than another business? You would think that it would be more efficient if government kept its hands off, but then you can point out that the American system is absurdly expensive compared to other, even universal health care systems. However, much of the inefficiency in the health care system in the US can also be attributed to government.
You would need some detailed experiments and a cost-benefit analysis to really determine what system would be more efficient and inclusive.
