A home warranty was included with a home I purchased back when it was a buyers market. I did end up using it to replace an entire AC unit. Fortunately the process was surprisingly smooth. They required me to pay a few fees out of pocket, including a refrigerant disposal fee, which was funny because all the refrigerant had already leaked out. I tried to argue with them about that but gave up because it was a small price to pay for a new AC.

Even though I had a good experience, I think it's better to save up an emergency fund for home repairs rather than rely on a warranty.