and even less so on a used car.

Most major items like a car follow a bathtub curve for failures. The rate of failure is high in the first few months after purchase. All of these failures would be covered by the regular warranty. Once the car is "broken in", the rate of failure drops and flattens at almost nothing (the bottom of the bathtub). An extended warranty generally covers this section of the curve. The failures only pick up again at the end of life of the car. No extended warranty covers this section as they know it is a losing proposition.

The dealers make a ton of money on these warranties and they are like sucker bets at a casino. When they pay off, people love them, but more often than not they don't pay off and the house makes a killing.