The problem is that in bad accidents, the damages far excede the assets of your typical uninsured motorist.
And at worst, the cost of uninsured motorists is a manageable sum of money, which can somewhat be avoided by careful defensive driving, and that still can be less costly if you are a good enough driver.
Medical bills and other costs associated with bodily damage from an accident (i.e. physical therapy, lost wages, etc) can be very high and far from manageable.
I don’t particularly mind the extra fee for uninsured motorists, in order to help defray the cost, except that it penalizes people who are very good drivers, and own crappy cars that they don’t care about
No state requires you to buy insurance for damage to your car or body. It's damage to other peoples' cars as well as damage to their person that must be covered, which IMHO is very sound policy.
Furthermore, if insurance companies are allowed to price their policies as they see fit, good drivers will not be penalized. The fact that you're a good driver will keep your premiums low. And like I said, you can always opt out of insurance on your own car.
I’m sympathetic to that view. I tend to support Virginia’s law, even though I am cognizant that it is not necessarily in keeping with a pure limited-government position.
BTW, most car insurance provides very little money for medical. They expect that if people have major medical problems, their own insurance will cover it, and the coverage in the car insurance is to pay for deductables and co-pays.
If you don’t have medical, or your medical insurance won’t cover the treatment you choose, then you can sue the insurance company. If you win, the medical cost turns into “liability”, and is covered by the much-larger liability.