Extended warranties are a high profit business. That’s why dealerships and salesmen push them so hard.
Extended warranties take advantage of the ‘bathtub curve’ of reliability. The bathtub is a curve that looks like, well, a bathtub with a slope on each end and a flat spot in the middle. The slope on the left represents early failure from defective components. The failure rate decreases over time as the defects are shaken out. The manufacturer’s warranty protects you against failures in this area of the curve.
Then you get to the ‘floor’ of the bathtub, where failures are rare. Once products get out of their early failure period, they tend to work reliability for a long period of time until parts start to wear out. Then the failure rate starts to increase, and that’s the right side of the bathtub curve.
Extended warranties sell you protection from failure during the period where failures least likely to happen. They run out before parts start wearing out, and the parts of the vehicle that DO wear out during that period are exempted from the warranty.
A lot of people think the extended warranty is just the manufacturer’s warranty with some years added on. But if you read the paperwork you’ll see that there’s a whole host of excluded repairs which were not excluded before.
One reason why the insurance is generally a ripoff is because there is an asymmetry of information between the auto company and the person buying the insurance. The auto company knows exactly how much each car on average is going to cost in warranty repairs - they have a huge collection of data to draw from. But the customer really has no idea. So they have no way of knowing if the price of the extended warranty is justified.
Also remember that the warranty is more expensive than it looks, because you start paying for it the day you buy the car, but you derive zero benefit from it for 3 to 6 years when the manufacturer’s warranty runs out. So you’re basically giving the car company a free loan for those years.
If you take the cost of the extended warranty and instead set up an equivalent fund in the bank for auto repairs, by the time your warranty runs out you could have several thoousand dollars in the account. That will cover you for all but the most unlikely large repairs - a blown engine or transmission might cost a little more, but you’ll have a good chunk of the cost.
Then when you get to the end of the life of the car, whatever money is in the fund can be used as part of a down payment on the next car, which will lower your payments even more. Then do the same thing with the new car.