I bought the Honda extended warranty on the strength of Honda's good name. The warranty covered a Mercury Mountaineer. The new Mountaineer was purchased from a company that owned side-by-side Lincoln-Mercury and Honda dealerships. After the Mercury warranty ran out, my heater/ac (temp) control would not work. No matter where I set the mechanical control, I got hot air only. The warranty covered a long list of specified parts that appeared to be comprehensive. As I recall, heater/ac controls were among the items covered, but the warranty weasel maintained that the contract covered the mechanism or knob on the dash only, not other parts of the control linkage that froze up or rusted in place. I've forgotten the name he used to identify the failed part, but it was definitely part of the heater/ac control system. A repair required removal of the dashboard, and took a couple of days, at a price over $1,000. The Honda warranty weasel claimed that the failed part of the control assembly linkage was not precisely specified as a covered component, so the warranty claim was denied. This type of contract is vulnerable to weasel-like language interpretation ... something I would not have expected from Honda.
Interestingly, a friend of mine purchased a virtually identical vehicle as "used", and had the very same problem. His aftermarket warranty was not from Honda, and his repair was covered.
I have heard that some warranties specify what is NOT covered, and that may be more workable. A buyer does not expect coverage for "wear items" like belts, hoses, tires, etc. However, the Honda extended warranty was clearly full of holes because no matter how many hundreds of items are listed as "covered", there are hundreds more that are likely not specified. So, it becomes a matter of trust and good faith to a large degree. My trust in the Honda name dropped sharply after this experience. Perhaps other companies are no better, but they should be.
I must admit that Lexus balked at repairing a bad trunk release mechanism on my ES300 under terms of their extended warranty, but they did agree to the repair after I grumbled about it. I was frankly surprised when they initially told me that it might not be covered, but pleased when they did accept responsibility.