Oh well, too bad you still have to pay for those accidents through your insurance premium - thats how it works. The only difference is that you either pay it over tax or via a private business that will try everything to wiggle out of paying for your injuries.
How much choice and control do you really have by having a private insurance? If you get hit by a car on the street, your kid trips in the stairs, you walk into a wall and crack a rib, the difference between your and mine is that:
1) I don't have to think about what it will cost me
2) I don't have to fully understand every aspect of my insurance agreement in order to understand what I am entitled to
3) I don't have to fight a insurance company if they don't want to pay for it
4) I can just relax, have a beer, and know that I will be taken care of if something happens
I am not sure if its a justifiable comparison, typically you don't end up with a food costs in the hundres of thousands or millions in the blink of second. It's not like you all of a sudden get a bill from Mickey D for someone showing a truckload of hamburgers down your throat.
I am not completely sure where you want to go with this argument. But as a Scandinavian I am very much comfortable with the state ensuring my access to health care, knowing I do not ever have to ever have to think about medical costs, health insurance or access to one of the better health care systems in the world for me or my family. We could very much bear the costs of having private health insurance, but its just one less (big) worry...
I do think that production of food is very much a state matter - and unless you knew taxes in the US today go towards ensuring safe and predictable production of food through i.e. agricultural subsidies. I would expect the state to ensure that the country have a viable and thorough plan to ensure food supplies.
But why do you have to think about this at all? Wouldn't it just be easier that this was provided by the state, so that all citizens could afford getting necessary health care. At the same time it would relive you of having to compare coverage, copays, deductibles or in general understand the full fine print of your insurance agreements. Most comparable industrial countries have found a pretty decent solution to this where you move the financial burden of many basic services (health care, schooling, etc.) from the public, over to the government - allowing all citizens to benefit from these, without having to wonder if the can afford it.
How much choice and control do you really have by having a private insurance? If you get hit by a car on the street, your kid trips in the stairs, you walk into a wall and crack a rib, the difference between your and mine is that: 1) I don't have to think about what it will cost me 2) I don't have to fully understand every aspect of my insurance agreement in order to understand what I am entitled to 3) I don't have to fight a insurance company if they don't want to pay for it 4) I can just relax, have a beer, and know that I will be taken care of if something happens