These are additional profit for a dealer who sells them, pushed heavily because the profit involved in selling the warranty often exceeds the profit margin on the car. Not surprising that they try to scare you with the possibility of expensive repairs. They are pure profit for the those sold outside of a dealership, that is to say the those sold by sleazy companies that harass you on your smartphone.
Although it happens once in a blue moon, it is very rare that an extended warranty pays the car owner more in benefits than what the warranty costs over the years. These companies exist for one reason and one reason only. That is to take in as much as the market will bear and pay out little or nothing. They are very skilled at finding ways to avoid paying anything.
A few months ago a customer was all set to get her alternator replaced on a Honda and then she mentioned she had an extended warranty. She insisted that this company was different and paid with no hassle. NOT QUITE! Against my better judgement and against our long term policy of having nothing to do with these, I agreed to work with the warranty . As was 100% predictable, the time spent dealing with getting the customer only a partial payment for her repair expense exceeded the time with hands on the car to repair it. So the majority of the time spent on this repair ticket we never got paid for.
I am sorry if this causes disappointment, but I will not make that mistake again!
Thank you for your understanding, Don