# 4 makes a very interesting point. In general, though, there do seem to be good reasons for thinking that people are literally more "invested" in a service if they have to pay something for it, even if the payment is a very modest "co-payment." However, wannam's point about preventive care is a good one.
Actually, I think the financial burden of health care on the individual is part of the problem. Consumers might be more willing to take steps towards preventative care if the cost wasn't so high. For example, some cancers can be caught earlier and treated much more cost efficiently and with much greater success. People are often unwilling to have the tests run to screen for these early stages of cancer because the cost is so high. If the cost of health care were lower for the individual, people would be more likely to invest their time in preventative care which would, in turn, reduce the overall cost of health care.
We have a moral responsibility to pay for the services we use. There is no quandary in accepting charity from people who choose to give it, but we have no moral grounds for using services and wilfully refusing to pay. As #2 notes, many people have no idea about the cost of medical procedures, and so overuse them, putting a burden on the healthcare system and using up resources that others legitimately need. Insurance is a method of deferring some of the cost -- you pay into the system, and then you use it if you need it -- but more and more people are going to the emergency room for minor troubles and then refusing to pay. We should conserve our resources, not waste them, and if we can pay anything at all -- I paid off a $500 asthma procedure over six months -- we have the moral responsibility to do so.
We already do have to pay to some extent, but this is a good point. If we knew how much various procedures actually cost us and if we could save money by not having those procedures, I think that Americans would be less eager to seek medical treatment for conditions that did not really require treatment. As it is, we do not know how much a doctor visit will really cost us and so we tend to overuse medical services.