Is the US health system free market? The government provides healthcare via Medicare and Medicaid for seniors, the people for whom life expectancy and healthcare quality have the highest correlation.
For non-seniors, the medical insurance system certainly sometimes doesn’t feel like a free market from the consumer perspective, but the insurance companies are private for-profit institutions, and the medical providers are too, so it may well fit the definition.
What do you mean by this? Fatalities among the young will have a much larger impact on lowering nationwide life expectancy than fatalities among the elderly.
( Describing various systems in various countries as either communist of free market capitalist is pretty simplistic, it's not much as a linear spectrum either )
I'd also argue that the foundation for a high life expectancy doesn't start with good health care for seniors .. unless the metric is "life support via artificial means" .. life expectancy is grounded in healthy living and excerise from an early age well maintained with good health programs.