Insurance is mostly for the car damage (both cars) and it is required by the law.
Not true. The mandatory insurance covers also healthcare expenses. Sure, in typical setting nowadays the costs of the twisted metal are greater and few broken bones and a night in hospital is indeed covered from our tax-funded healthcare system.
BUT when someone is seriously injured, and suffers a trauma that causes disability and makes then unable to work or a need to train themselves to a new profession, our system definitely does NOT cover those, and those and funded from your insurance. And these are the big bucks, google what courts have awarded for loss of ability to work in these cases... (And if you are uninsured or there is malice the common insurance pool which pays these damages will go after you for those damages...)