I bought the extended warranties in three circumstances:
In the '90's and into part of the '00's, my experience with laptops was that every one of them across multiple brands and users failed in some way before an extended warranty's period ended. And that included a startup that grew to as many as 80 people. Yes, the more abusive users had more problems, but even the gentle users did too. And IIRC, even CR recommended them then in this particular case. I had all manner of parts replaced under the warranty during that period, and it paid off. That said, this has become much less true in the last 8 years or so; I don't believe they pay any longer. This was never true for desktops, which have had readily available replacement parts for cheap (so I didn't cover those).
I bought a TV for my ailing mother, wanted a turnkey experience for her if the TV failed, and I wasn't close enough to be able to deal with it if the unit died. The TV didn't fail, but I received the peace of mind I purchased.
The third case was a little different: a home warranty when purchasing a house. It was pretty clear on inspection whether some of the appliances were close to their EOL. And the bonus is that through negotiation, one can often get the seller to pay part or all of the premium. Made money on that one too.
I haven't bought extended warranties on anything else, and it's paid off.
Oh, one special case: I skipped the extended warranty on tires for my car one time, and discovered (very soon after purchase, fortunately) that the installer had drastically over-inflated the tires, which would have, of course, caused accelerated and non-uniform wear. I suspected such nonsense and checked before I'd driven very far, and reduced the pressure to spec. "Coincidence? Perhaps! You be the judge!"