We know. You're a very excellent driver. There's no way you'd ever be at fault for an accident. Even still, there are idiots out there. You've met them before. They are the ones who block your commute every morning. Being prepared for when one of those idiots eventually hits you (it will happen) is important, and can save you from both having to pay money and perhaps having to spend time in jail.
Jail time? Jail time? Why yes, jail time. If you are in an accident, and not taken to a hospital, you are required to stop at the scene of the accident. If you take off before the police arrive or fail to exchange information, you can (and probably will) be charged with a hit-and-run, even if it's the other driver's fault.
A hit and run can be a felony offense in Illinois if someone is injured, or a severe misdemeanor if only property damage occurs. Either charge can result in more time than you'd like to spend behind bars. It doesn't matter who was at fault in the accident, or that the meeting you were rushing to couldn't be postponed. Leaving the scene of an accident is a crime.