People will respond negatively to "if you can't afford it, you can't eat". But the government doesn't run farms and groceries, not even by "supplementing the private market". They give you food stamps. Why can't the government give you healthcare vouchers? Why do they have to set up their own insurance plan?
Like I said health care is sometimes very expensive. Way more expensive than food. That's why people are willing to pay for health insurance, and why insurance companies don't even offer "starvation" insurance that would, say, let you get all your groceries for free with some small co-pay. There's not enough variation in food prices over a range that we care about for our risk aversion to kick in.
So you are comparing food to insurance. Maybe part of the problem here is that people keep conflating government insurance with government-run health care. They are not the same. What's happening here is that the government is seeing a product that the private market is not providing, but society has deemed desirable for everyone to have. That's a pretty clear prescription for a government option (like USPS).
Why does the government even have to run an insurance company though? Why can't they give you insurance vouchers?
"Starvation insurance" is indeed a bad idea. So is "insurance" for routine care. It costs a relatively predictable amount of money to have a routine annual blood test and physical. Why can't I just pay that money myself, instead of paying an insurance company to pay that money for me? And if I can't afford it, instead of having the government set up an "insurance" company to buy me doctor visits and a dental plan, why can't they just give me vouchers for that too? Save the "insurance" for stuff that actually makes sense to insure against--things like hospital visits and so forth.
