Your first sentence is "In the popular telling, there is a strong and reasonably constant relationship between health spending and life expectancy.". My comment was that I am not aware of this being the popular telling. But instead from what I can tell most people agree that the US doesn't deliver better results despite much higher spending.
Otherwise I think you have dug up a good and useful amount of data although I think some of your conclusions are debatable. This is probably to be expected if you analyze such a complex system.
The question that arises for me from the article is: what should society shift spending towards/away from healthcare to receive the most life expectancy gains? Fight obesity, transport safety, drugs? Is any areas of those amicable to be solved by spending?
Donu you also suggest that high levels of health care spending are more effective than we might expect since the wealth that allows more spending also come with higher obesity and larger overdose risks?
Is there one of your charts that indicates which countries have seen the best returns from higher levels of health care spending?
Maybe try actually reading it though?