Mod up parent!
To me, it's a question of economics. And for those sorts of questions, I go to people who know something about how it works, rich people. Particularly rich people who made it rich when they were young and managed to hold on to that money. I know a few of those, and none of them buy extended warranties on products, they self-insure. Granted, they have the money to do so. But, if you buy 2-3 extended warranties per year (that's $400-600/year), you could drop all that in a savings account and afford to replace 1 of those 3 big-ticket items every 3 years (I'm assuming a warranty is 10% of the sticker cost), which is probably how many times those extended warranties would have to completely replace your product. And that's full replacement mind you, that doesn't account for when it just needs a $100 or $200 repair, which if that is all you needed, you can do that 3-6 times a year.
Sure, there will be some bad years, but that's why you have a general emergency fund as well to soak those losses. And, all that money is sitting in your bank account earning you interest (keep it in the right kind of account and it could earn anywhere from 8-12% and still be accessible like a checking account), not some big insurance company.