Not exactly.The same argument applies also for other insurance - home, flood, auto, major medical, long term care, ...
So far, we've been fortunate never to make a major claim to any of our insurance policies. So, we would have been better off in not purchasing those policies and putting the cost savings into a "rainy day fund" - which would by now be pretty significant.
But if we did have a major claim on any of those policies, it could cost us more than the rainy day fund.
The extended warranty, like any insurance, usually benefits less than half of the customers, who end up getting hit with his costs.
If you don't buy the extended warranty, there's likely a (slightly) better than 50% chance that you'll save $$$ by paying for the out-of-warranty repairs yourself. But there's also a (close to 50%?) chance that your out-of-warranty costs could be higher, and in some cases, much higher...
We purchased the extended warranty on our 2017 S and 2018 X and will likely keep each until we get close to 8 years or 100K miles.
major medical could be unlimited high. House and flood is still worth it.
With a car, you know the limit. Worst case, scrap it.