Here in the US, our insurance companies are not in business to pay for auto accidents. They are in business to collect our money. Hence the tiered pricing for different dollar amounts of coverage. Also why most insurance companies will cancel our policies if we have more than one accident in X number of months. Then the high risk insurance steps in for hundreds of dollars per month. Your system sounds better.
One important difference: in the US you get a license by memorizing a few signs and traffic laws. They will tell you "driving is a privilege, not a fundamental right" but in practice it's treated like a right unless you get multiple DUIs or something (even then, a few years later - or less - the irresponsible adult can re-apply). The result is lots of unskilled drivers on the road, including those with more than enough experience to know better.
It's regrettable but the more the USA continues down its current commercial and philosophical path, the more people tend to do the minimum even when the minimum (in this case, of skill) is grossly inadequate. It doesn't take much effort to gradually get just a little better at something day by day, but it does take an awareness that one should do so. Here driving is widely seen as nothing more than a means to an end, not something in which to invest any skill because the lives of oneself and others may depend on it. Actually almost everything is viewed that way. It's the same reason in computing, there are so many permanent newbies - they managed to avoid accidentally picking up any new knowledge day by day even when a computer is an important tool without which they can't earn a living.
So unsurprisingly, I see unsafe practices every day I drive. Also, stupid unnecessary shit like tailgating 2 inches from the other guy's bumper with two open passing lanes is unfathomably popular. On a related practice, I have no idea why it's so important to get beside somebody and carefully maintain the exact same speed, even though to appear there they had to initially move faster, but I simply cannot drive a few miles down an interstate without seeing it, even during low-traffic hours like 4am. I think it's just a mindless "go with the flow, do what everyone else is doing" herd mentality -- that's consistent with what I see elsewhere in this culture. It could also be some psychology of feeling powerless in one's own life, causing them to want to control others by blocking passing lanes and creating hazards. Also, during heavy rain, many don't seem to understand that visibility is vastly improved by not hanging out in the massive backwash from 18-wheelers; this is really not difficult to comprehend, but to do so, one would have to be aware enough to consider it.
As I entertain no delusions about controlling what other people do, my main goal while driving is to keep as much distance between myself and others as I can. They can drive in tightly clustered packs with no room to maneuver (and sometimes, terrible visibility) if that pleases them. Whether it means speeding up or slowing down, I'll be the guy between the nearest two packs.
Please educate me if I am wrong, but I understand that in most European nations, acquiring a license means you actually have to demonstrate skill with maneuvering the vehicle and it's not nearly so easy. The failure rate for license applicants is significantly higher, and since driving means we're talking life and limb, that sounds quite reasonable. If you have only driven in Europe you might even find my descriptions difficult to believe, but I promise you I see this and worse every day.
TL:DR right? I really think it boils down to culture. The USA once had a culture that promoted responsible adulthood but that was a long time ago. What's promoted now is convenience and the idea that nothing is ever one's own fault. The focus has shifted from responsibility to a childish concern about fault-and-blame that prevents so many from learning that cause precedes effect. It's really amazing how many things boil down to that. Ergo, what works great in Europe might not work here, even if it really should be that way. Would you offer unlimited liability coverage to these people? While I don't normally advocate using technology to solve social problems caused by human stupidity and irresponsible adults, I really cannot wait until fully autonomous self-driving cars become mainstream.