The folks selling you the insurance don't do a great job of explaining to you why you need to buy higher amounts of uninsured motorist coverage. Look, its the cheapest extra insurance you can buy.
When you are in a car accident your health insurance company is, in many cases, going to look to be reimbursed for what they paid for your medical bills. You need to make sure there is enough insurance money to go around and its YOUR responsibility to make sure you protect yourself and your family.
If you are seriously hurt, and you visit a lawyer who reviews all of the insurance, and it turns out that there isn't enough insurance to adequately protect you...its YOUR fault. Its not the other person's responsibility to adequately insure themself. In Virginia its perfectly legal to drive WITHOUT insurance.