what's the relevant distinction between health care spending and spending on airline travel? There is one and it's that so much of health care spending is people spending other people's money
This is quite right. I say that Americans make extravagant use of medical procedures with high costs and low benefits. But that is only a social problem to the extent that we socialize it.
Under a free market health care system, if you go for an unnecessary MRI, that does not affect me any more than if you buy an unnecessary television. Getting rid of government health care provision gets rid of health care costs as a social problem.
However, I think that in reality we will see a lot of collective subsidies in health care. If you took away government, then my guess is that a lot of charity would go toward health care for people with low incomes, and those charities would have to come up with rules for rationing their budgets. So I think it's inevitable that at least in some situations there will be people involved in making medical decisions beyond just the doctor and the patient.