I use the American Home Warranty for all my inspections. I have actually had one claim for my client, which I helped them file.
AHW covers for 90 days after the inspection or 90 days from closing, whichever is longer.
In my case, the client didn't move in immediately after close, but did some work on the house. The previous owners had not had the A/C unit serviced in a long time, and the condensate started leaking around day 85 after close. The sellers had piled belongings and stored stuff so that I could not access the air handler. Thankfully, I documented this in my report.
The condensate leaked out, and did some damage to the wall.
AHWA does not pay for the water damage-just like most homeowners insurances - but they did pay the claim to have the A/C unit cleaned and serviced, to the tune of a couple hundred bucks.
I think it's a great service, and I recommend it to anyone.