Whoever said that insurance companies don't go after individuals had no idea what he or she was talking about.  Insurance companies deal with individuals on an adversary basis every day.  And if the insurance company thinks it has a valid claim against an individual, with a reasonable chance of success, more often than not it will assert it.

The law requires you to be financially responsible for the consequences of your driving, and you can satisfy that by having the required insurance.  If you don't have insurance, you have to demonstrate that you can pay for the damages you caused, or you will lose your license.