A few points...on the OP there are plenty of things the government does in the US, that doesn't mean they do it Well.

to the more specific
Healthcare will always have to be denied, the question is
who sets the criteria for denying care?
who pays for the care?

The answer to both of those questions should be the same

If it is the government, then you have the problems of lack of choice and tyrrany of the majority
If it is individuals, then they have the problems of the random factor of medical care needs

If it is an insurance type organization, then the problem is
difficulty of making an understandable contract as to the value of healthcare to be provided
as well as the fact that medical problems aren't the same as your house burning down... they are problems that linger for a long time both before and after 'discovery'.

That is also the problem with malpractice insurance.

It might be worthwhile to have a "federal medical standards board" that recommends generic 'best practices' and evaluates the probable Value of certain medical care options. This might make insurance plans a bit more comprehensible, making it more like a real market. It could also make malpractice insurance cheaper.