First, we don't have a healthcare system. We have a sick care system. Our system is structured to discourage people who aren't horribly sick from seeing a health care professional. We don't see doctors in this country to maintain good health. We see them when we're so sick, we can't fix the problem ourselves, at home, with an over the counter drug.
Second, every aspect of our system is for profit. Hospitals, insurance companies, and drug companies all want to squeeze the most money they can out of the people using their products and services, at a time when many of them can least afford it. We pay double, triple, quadruple what other countries pay for the same products and services because there is no regulation on what these companies charge. Making the obscene profits they do on the backs of people who are ill, and in need of care or medication seems to be just fine in the eyes of many Americans---until they're hit with the bills themselves.
Third, America seems to be in a phase the demonizes people who don't have the means to pay for care. The whole country seems to have an "I've got mine, so to hell with the rest of you" mindset. Profit and money are good, and caring for your neighbors and those who are less fortunate is bad. Until we turn that around, and decide that healthy people contribute to a healthy society, and that caring for those with least should be more important than how much money a corporation can squeeze out of them, we're going to continue to be ranked at the bottom of those surveys.
Good health care should be a right for all, not a privilege reserved for the rich. The countries who rank highest in those surveys have recognized this, and acted upon it. America has not.