If you look at pretty much any general population level outcome, a country with a high concentration of health insurance (as proxy for financial resource to get healthcare) is going to have bad "average" outcomes.
If you look at metrics that select a sample that tends to have access to healthcare (e.g., cancer tends to cluster in over-65s, who have access to Medicare and, at greater rates than the general population, Medicaid), you're going to get a look at "what the healthcare technology is like in that country for people with access to it."
It's entirely fair to point out that average outcomes suck for average people because "average" access to healthcare is "really shitty access to healthcare."
It's also fair to point out that if you change how the system operates, it's not unreasonable to ask whether you'll change the system's strong points, which may well be "technically sophisticated care for those that actually have access."
My position on this is a third, orthogonal position (which is that how you pay for care and the operations that produce that care are not unrelated, and fractured, free-market operations produce fractured care, and that operations have much more day-to-day impact on healthcare outcomes than technical sophistication.) But it's unrelated to the above.
2. What percentage of poorer "health outcomes" are due to the US's ~33% obesity rate and overall horrid diet and have nothing to do with care or access?
Obesity and diet are very much related to care and access. If you can't afford to go to the doctor unless you're dying, nobody is going to tell you when your cholesterol is getting too high and you should adjust your diet, or your blood sugar is getting into the warning zone, or whatever.
We have such high obesity because we don't focus enough on preventative care, and lots of people can't afford preventative care even if they want it.
I have a hard time swallowing the idea that obesity and diet are related to access to medical care. Our great great grandparents undoubtedly had far less access to healthcare than even the average lower class, modern American, and yet obesity was almost non-existent for their generation.
Occam's razor would say that an epidemic of diet related illness is caused by a societal shift in diet. The simplistic boiling down of the complex answer from nutrition experts is that the massive increase in processed foods in the American diet, post WWII, along with the insane increase in sugar consumption, have led to the obesity and diabetes epidemics (and increasingly believed to be one of the main causes of cancer).
IMHO we could do exponentially more for the life expectancy of poor Americans by solving the problem of food deserts than by upending the entire medical system, that is functional for the majority, for a wholly bureaucratically controlled system - which, by the way, will eventually have to include decisions on which people do not get access to treatment.