...It IS possible to look at the average cost of repairs over a specific time frame to see if a warranty is worthwhile
As in Casino gambling, lottery, insurance (including healthcare, dental...), and, I suspect also, ESA (extended warranty)... the house always wins in the end as a whole.
On the average, if you pay to play in those games, the odds of recuperating your investments are heavily against you.
So why do people still participate in them?
Some may not understand. If they see lottery winners on newspapers, they might think they can win too!
Some do understand, but they feel there's value in losing their investment. They may lose in Casino but they feel the entertainment is worth the cost.
Others don't get cancer, house fire but they still are happy in losing their investment because they feel that's the cost for the peace of mind.
I myself bought all ESA that's been offered to me for 2012 Model S, 2017 Model X, (and still waiting for the offer for 2018 Model 3).
My 2017 Model X and 2018 Model 3 have been troubled free.
However, My 2012 Model S had 3 services in its old age and covered by ESA.
1) Mobile Connector Unit: Pre-emptivly replaced due to signs of overheat at the connection points. Notice that ESA now excludes this coverage= $500.
2) 17" display and its computer= $4,000 (The screen alone without computer is cheaper).
3) Cabin heater (for human, not battery pack) = $4,500
So, in my case, my investment paid off very well. But even if my car didn't need repairs, I am still glad to pay for ESA for the peace of mind: Pay once in advance and to guarantee to limit my loss in future.
Thus, it's up to how you want to manage the unknown future risks.