However, diabetes, broken ankles and heart disease are not a public health
threats, which means that the government has no call to impose the costs
of
treating such individual illnesses on others, because there is no exported
harm that justifies imposing this burden on others.


You don't think so? There are many ways that society pays the price for
illness beyond the obvious issues of contagion and health care costs. The
economic costs of so many Americans sitting at home because they're sick or
injured is astronomical when you consider things like lost productivity,
overinflated payrolls forced upon employers (which transfer those costs to
consumers), etc. When you're a small business owner and your employees are
home sick instead of working, you lose money. So does the national economy.
It's been a long time since I've seen estimates of the figures, but they're
enormous.