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
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