Maybe. But that 1 in 100 has actual peace of mind, because nothing is peace of mind like ready cash. I don't need anyone's permission to do the repair, I don't have to fight with anyone about if the failure is covered, I don't have to only use certain mechanics, I don't have to use only certain parts, I can modify as I see fit, etc. If you (generic you, not you in particular) lack financial discipline and don't care to pay others to assume your risks, then warranty peace of mind is likely the best option remaining to you. If you're willing to be disciplined, you'll have more money and more peace of mind in the long run.
I've been poor, like living in a literal shack in the woods with no running water sort of poor, and I've been "affluent", as the marketing demographics label me. I prefer the second. I didn't get here by winning the lottery or by getting some exceptionally high paying job. I just didn't buy into keeping up with the Jones, especially when it came time to buy a home, wasting money on things that don't matter, etc. I lived a pretty ascetic lifestyle for a few years to get my feet under me, worked 3 jobs for awhile, busted my ass in other words, and now I can pay cash for my Power Wagon, travel abroad once or twice a year, and carry no debt other than my mortgage which makes no sense to pay off. All while raising a family on one salary and saving for an early retirement. Finacial knowledge and discipline are power.
So, again, everyone is in a different place, but my recommendation is still to avoid extended warranties. Learn to save, self insure, have more money long term.