Sorry, I'm used to people citing actual sources rather than information based on sources. But, going in to read the basis of the rankings we see (in real time):
I'm through half of the document and as yet, there's been no real evidence or basis for the ranking. I do see, "It is especially beneficial to make sure that as large a percentage as possible of the poorest people in each country can get insurance," says Dr Frenk. "Insurance protects people against the catastrophic effects of poor health. What we are seeing is that in many countries, the poor pay a higher percentage of their income on health care than the rich." This tells me that the WHO is making a moral observation, rather than any observation based on the quality of care. The poor pay a greater portion of their income on anything that they buy than the rich do, that's not a valid critique of a health care system.
This is interesting, and telling: "In designing the framework for health system performance, WHO broke new methodological ground, employing a technique not previously used for health systems. It compares each country’s system to what the experts estimate to be the upper limit of what can be done with the level of resources available in that country." So, the WHO isn't making a judgement based on how efficient the health care systems are, how well they treat people, how well they keep the sick alive; it's how well the WHO opines that they could do based on their GDP. That would explain why so many poor countries rank higher than the U. S..
The the qualitative measures: 1) "The nations with the most responsive health systems are the United States, Switzerland, Luxembourg, Denmark, Germany, Japan, Canada, Norway, Netherlands and Sweden." Great, so we're responsive.
2) The DALE measure (life expectancy) puts the U. S. in the top rung with other developed nations.
The other measures used in the study you cite are not actually measures of health system effectiveness. They are measures of what the WHO considers a fair and just health care system. Among the first things explained in the study is that the WHO believes that health systems should be supported by tax dollars (the WHO fundementally believes in socialized medicine). In areas that the WHO measures actually quality of care, the U. S. does well.
So, you found a biased study that supports your view. Good job. But remember, it only supports your view by having a 2:1 ratio of nominal measures to quantitative measures.