Yeah, but if the US had a single-payer healthcare system, the government would also have an incentive to ensure that doesn't happen as much - so it would take a much better and stricter look at what "food vendors" are allowed to sell in the US and what they can put in their foods or even how transparent they are about it.
Right now it has very little incentive to do that because Americans being fat and sick is "not the government's problem". It's the people's and insurance companies' problem, which is why insurance companies fight to be responsible for treating as few conditions as possible.
If the US had a single-payer healthcare system, it also wouldn't be the only country in the world that "doesn't believe" in climate change and "wants to save coal jobs" or even fracking jobs (in case you thought I was only referring to Trump's policies).
I wonder, does the US goverment (state, local or federal) insitute programs for physical excerise/sports?
my goverment does this, especially with children and teenagers/young adults (the first two also have mandatory P.E Classes in school, and outside of school, sports is usually subsidized for the poor).
Getting people to live healthy at a young age results in people living healthy when they are adults.