We had AHS when we bought our first home.
The hot water tank went out within 6 months. We paid only $50 to have it replaced. We also had a couple sewer clogs that cost us $40 or 50 out of pocket. AT the time we were going from renting to owning for the first time, so it was good for us.
Since then, we are used to fixing or replacing one major thing every couple years anyway, and the long-term average is probably less than the warranty covers, so I no longer use these.
Frankly, if you are a first-time buyer, take the warranty. It allows you to enjoy the honeymoon period in your first place.