What "society" (government) can do is force everyone to share THE SAME risks
single-payer insurance == monopoly
So the freedom we're really talking about is --- notionally --- the freedom to make what basically must be an irresponsible choice.
It's true; single payer systems do create a monopoly for health care funding; that monopoly takes its place alongside the monopoly for military force, for air traffic control, for fire prevention, for oceanic weather surveillance, &c.
I don't think this is a significant problem, because the people who receive this subsidy vastly outnumber the people who provide it.
Edit: A liver transplant is a procedure with a very high expected value in terms of QALY/USD. Americans in aggregate spend a great deal of money and effort on procedures with very low expected QALY/USD. Some people, myself included, would prefer not to purchase a procedure with very low expected QALY/USD.
There was a good discussion on a similar subject earlier: http://news.ycombinator.com/item?id=3313570
That's true, but it's not a winning argument.
"Part of the notion that suggests people should be forced into sharing those risks is that nobody can rationally rule out future unbounded <whatever> expenses; you can't predict the future, and virtually nobody has enough money to cover every plausible <whatever> expense they might face."
Meet socialism.