In other developed countries, the market is also saturated with fast food and the population has a high proportion of overweight people. The epidemic of adult diabetes for instance is not just an american phenomena but affects almost 9% of the population of Europe. They still have a higher average life expectancy. Some would say its skewed even further because here in the US, drastic attempts to extend life are made even when quality of life is gone, whereas many european countries are more comfortable letting people go once quality of life is gone.
I think the big difference in a socialized health care system is preventative care. Here in the U.S. a lot of preventative care is not covered by insurance. If you have a high deductible, or no insurance, you don't generally even go to the doctor unless you are seriously ill. We spend most of our resources trying to treat catastrophic health problems instead of preventing them in the first place, though we are getting better.
That said, I don't see how socialized health care would work in the US without major system changes. It's an economic supply/demand issue. As big and clunky as our system is, it can hardly keep up with the patients it has now. Most adults I know have to wait at least a month (sometimes 2 or 3) to get an appointment scheduled. Opening up health care to all would result in the same thing that happened when the U.S. tried to regulate gas prices in the 1970's resulting in the oil crisis. Price fixing always results in shortages. The number of doctors and nurses in the US would have to grow dramatically before we could reasonably handles all the new patients in a reasonable amount of waiting time.