Yes. Healthcare is a service; nobody is entitled to it. Even if we disregard that, ultimately under a government-funded care system care will be of a poorer quality than it will be under a free-market system for those that can afford it, and I don't think we should not allow people to buy the better healthcare they can afford.
Merely saying that something is a service doesn't by itself imply anything about how that service is best delivered. One could easily say that the military is a service too; that by itself implies nothing about how to finance and organize its provision.
Regarding the second point you make, I actually agree that private competition in health insurance improves the quality of its delivery and that people who can pay for more coverage should get more. I think, however, that when such private companies are for-profit ones, that's where the skewing of incentives comes in, because it leads to things like recision and purging. Recision and purging do allow insurance companies to survive, but I think it's much harder to argue that they create efficiency in the delivery of the product. Insurance enables people to pool their risk, some some who are covered will use the coverage they buy and some won't, but recision and purging bar some people from the even the chance to pool their risk. In this case, insurance companies survive not through the optimal delivery of the product to the greatest number of buyers, but by
barring some people from even buying the product. That, while certainly not the only reason, is one major reason why only 57% of the American public are covered by private insurance plans (27% are covered by government plans and 16% are uncovered). That kind of figure strikes me as a major efficiency fail. With numbers like that, I think a government has to step in and either provide coverage for uncovered people directly or subsidize those who can't afford coverage so companies can cover the costs of the larger risk pools. The alternative would be to have very, very large numbers of people in society walking around with no health insurance coverage, and, for a large host of reasons, many of them economic and not just moral, that would be quite bad.
