Having had problems with water heater, leaking shower, garage door, and refrigerator door in a house we purchased I have had an adequate trial of AHS -- according to AHS, not a single one of these problems was "covered" under the warranty. AHS has carefully sculpted their coverage so narrowly that they can evade the majority of costs -- so narrowly that common and routine issues you are likely to face will not be covered.
The warranty is no such thing. I strongly recommend taking the 5 or $600 and setting it aside for yearly routine costs.
They should be investigated! It's a massive scam.
Product or Service Mentioned: American Home Shield Warranty.