The point is to allow people to make their own choices. What you're advocating is depriving people of the choice of how to spend their money and manage their risk/reward options.
You want other people to suffer a higher risk, just so you can save money.
And no matter how often you try to frame it as a matter of "I choose for myself", you're actually choosing for others.
That's highly illiberal and unfree, by the way.
I'm amazed that there are actually people who think it should be okay to drive around uninsured, so when you hit a pedestrian and he ends up a quadriplegic and in need of constant care, you just say "oh, I'm sorry, take all the ten thousand Euros I have and good life to you!".
I'm certain you'd see the stupidity of your point of view if you were the quadriplegic without any compensation.
Fortunately, in Europe we don't let those people learn their lesson the very hard way. We do the sensible thing and just demand insurance from everyone. Including self-proclaimed libertarian rebels against the system.
It is my choice whether to insure myself or not. It is the choice of the driver whether to insure himself or not. It is the responsibility of the road owner to demand all cars have insurance. Unfortunately, we mostly have only one road owner these days: government. If you had plenty, then some would allow uninsured cars and some wouldn't. Then it would be up to both drivers and pedestrians to use those roads (this is one possible solution).
You're trying once again to draw an image of a libertarian as a ruthless individual who doesn't care about the misfortunes of other people. I do care very much about that and I would be happy to help out. What I am against is FORCE with which government demands people operate in the market very often against their will.
Some people are riskier. Some people are careful. As long as it doesn't affect another person, everyone should be free to do whatever the hell they want.
Finally, your elitist standpoint "we in Europe" is simply disgusting to me. I apologize for this emotional outbreak, but I have zero respect for collectivism. "You in Europe" are all different and by saying it they way you did, you simply disrespect people who have opposing views, not considering them a part of your society.
I'm almost always on the side of less governmental power, but to believe that all regulations like these are unnecessary is just boneheaded.
But you do. And when you choose to use a public service, you should obey the rules set forth by the governing body of that public service. What you are suggesting is that you have the right to decide what to spend your money on, but when others do it, it's wrong.
You are the one complaining about using public infrastructure and having to follow the rules when using it.