If you don't put gas into your car, it does not run. The chances of the car incurring thousands of dollars of damage is negligible. The insurance company will pay for the routine shot or exam since they both help to avoid medical complications that would drive up the cost of care.

Granted, the comparison is imperfect. Medical insurance won't pay for a healthy diet (another way to reduce health problems) and replacing the brakes on a car would reduce the chances of an accident causing thousands of dollars of damages ... but we are human, and sometimes it is a miracle that we even take half measures.