I would say it is a privilege, but that it should be a privilege available to people who live in a civilized society, if they need it even if they are in a (temporary) situation where they can not pay for some/all of it.
I don't think the US system works as well as it could for the good of the whole of American society. I would also add that I think the system in the UK (and Europe) could also be critisised in the same way, but from the opposite end of the spectrum.
I do believe that it should be possible to provide a system that lies somewhere between the ideas of free healthcare for all as is attempted in Europe (and is helping to bankrupt the countries) and the American ideal where the most needy of society can fall through the gaps. Both systems have some acknowledgement of the benefits of a "middle road" in the UK private healthcare is quite a big business but the demands put upon the government run "national health service" are still too wide ranging and costly. For example I do not think sex change opperations, cosmetic surgery and fertility treatment should be paid for by the state. Two of those are "personal choice" issues and for fertility treatment, IMHO if you can't afford $2,000 for the treatment you damn well sure can't afford to have kids because the total cost is astronomical. In the US you have Medicaid, but IMHO this does not cover sufficient cases and can be too hard to qualify for.
I'm not a socialist by nature and I do not like Governments interfering in the day to day lives of it's citizens, but IMHO health and education are two areas where the issues are so large that, in any civilised society, there needs to be an institution that makes sure the interests of all are catered for. There are, IMHO two issues as to the payment side of things one is the individuals ability to pay for his or her healthcare and the other is a societies ability to pay for the needs of it's members. There are a number of ways where that can work side by side to give a better answer to the needs of the individual and of the society.
I think the best system is one where there is a basic level of healthcare available for those that need it (better and more widely available than Medicaid) , this can/should be coupled with a private medical system that (obviously) would offer a better standard of comfort of treatment and a wider range of treatments. This private medical should receive decent tax breaks (not completely the case here in the UK) to encourage people to make their own provisions.
I can't argue with you that something should be done to try to make healthcare more affordable, but, IMO, that stems more from problems with excessive and outrageous lawsuits that the medical profession faces these days (but that's a different debate altogether).
I agree 100% with this comment, unless the US finds a way to deal with the ridiculous levels of law suits and payouts it's going to be very difficult to come up with a viable system that is going to benefit ALL the people of America.