Like any insurance, it's a numbers game - homo economicus will gladly pay an extra 10% for extended warranty if they believe there's a >10% chance it will require replacing in that time.
Of course, those selling the insurance know the numbers best so it generally works to their advantage, which (in association with consumers who lose / forget their warranties) is a big revenue boon to retailers, as you note.
Recognising when you are an edge case helps - I always buy extended warranties on microwaves, because I'm a once-a-month-cooker who therefore uses the microwave a LOT more than the average consumer, and that bet has paid off for me several times now.
Of course, those selling the insurance know the numbers best so it generally works to their advantage, which (in association with consumers who lose / forget their warranties) is a big revenue boon to retailers, as you note.
Recognising when you are an edge case helps - I always buy extended warranties on microwaves, because I'm a once-a-month-cooker who therefore uses the microwave a LOT more than the average consumer, and that bet has paid off for me several times now.