1. One of the problems with treating healthcare as a right is the fact that enjoying it requires the labor of others. Unless one can have the right to the labor of others, one cannot have a right to healthcare. (Or to jury trials, for that matter, but juries could more easily be provided on a voluntary basis than healthcare.)
2. AndrewStebbins mentioned the lack of prevenative care. I think this is largely a product of perverse cost incentives--it's simply cheaper on average to wait until an emergency, if one happens. I'm not sure how to solve either without forcing people to pay the true cost of ER visits, which would be politically suicidal to propose. There's also a problem with unhealthy lifestyle choices, which I'm not sure how to solve without coercion, except perhaps lifting government subsidies on unhealthy things like corn syrup and lifting duties on imports of healthy foods.
Another problem with healthcare costs is the overregulation. For instance, a new prescription drug sits unavailable for at least 10 years after its development before it is even decided if it will ever be available to the public. Imagine if every time a new car was developed, Chevy had to wait 10 years before finding out if it gets to sell it. Car prices would skyrocket. Once drugs are finally produced, the prescription drug laws work to keep prices high. For instance, I take a prescription that costs $60 each month. There is another drug on the market that is the same exact medicine in 4x the dose. This drug, however, can only legally be prescribed for an ailment I don't have. It's cost? Also $60. Were this restriction lifted, I could purchase this second pill and a pill-cutter, instantly getting the same benefit for 1/4 the cost.
Another problem is that much of our healthcare expenses are guaranteed by the government programs, so there is no incentive among providers to keep costs down. (We see the same problem in the cost of tuition at universities--subsidized loans guarantee money for schools, who in turn have little incentive to control costs.)
3. If costs correlated with benefits, water would be the most expensive thing on earth.
4. The solution is not universal healthcare. Healthcare, unfortunately, has finite availability. When you give scarce things away for free, you run out. The task is to figure out the most efficient way to distribute the resources that we have, and central planning and single-payer systems (in any industry) have had a dismally poor track record throughout history.
One thing I think would do a lot is to lift most of the regulations on healthcare and allow patients, if they choose, to seek riskier treatment options (e.g. experimental or unapproved drugs, doctors with lesser credentials, etc.). We could also alter the law for drug patents adding a mandatory licensing fee, like we have for certain copyrights. That way generics could be available from day one while still offering the patent holders at least some protection.
I cant really get too involved because I dont have the time to sacrifice but I do have to chime in alittle on your #2 comment...
Preventative care is undoubtedly much less expensive that ER care. ER care involves many more costs than does a regular check-up at a family doctor. Many people do not have regular check-ups because they cannot afford to pay out of pocket; instead, they wait til something serious happens and then they go to the ER where they will not be turned away. Well... Someone pays those salaries of the people who take care of this uninsured person and it is incidentally the people who HAVE insurance. Why not make preventative care available to EVERYONE and eliminate these types of inefficiencies... Also, the overcrowding of ERs for headaches and "back pain" hurts those who HAVE health insurance and HAVE emergencies. I don't want to wait 3 hours in an ER waiting room because I cut my hand and 10 people are trying to score OXY's.... I know I probably sound like I am regurgitating something that could be discussed on Bill Maher but the fact is that this is reality. There may be no perfect system of medical care for our country but I think we can agree that the one we have now is DEFINITELY not good, nevermind perfect...... We think that we are the "gold standard" example of how countries should be run but this is a complete delusion. The reality is that healthcare reform isnt being challenged because it is "bad" for american citizens; it is being challenged because it is SOOOO GOOOD financially for SOME citizens.... eh hem... Politicians....?