Peace of mind Vs. individual risk tolerance Vs. $ Vs. statistics....first two will be different for everyone. Also depends if you are a DIY person.
Statistically you are likely to loose out by purchasing a (reputable) extended warranty Vs. self-insure ...dem actuaries are purty smart

....but one or two big ticket items would make it worthwhile. The probability of 'stuff' going wrong for a 6+ yr old X is also more likely - 'coincidentally' just after the original warranty + CPO expires....more of them smart actuarial types counting the future beans.
No doubt you will get answers on here from 'Def. yes, these beasts are $$$ to repair, and I have already saved $$$ over the warranty cost" to 'Def. no, I spent $$$ on the warranty and have only used it x times'.
I would just self-insure but YMMV...your roll of the dice