Insurance exists to transfer risks you cannot survive. That gives a simple decision rule: insure what would ruin you; self-insure what would merely annoy you. A house fire, a disability that ends your income, a serious illness, liability for injuring someone — these can be financially unrecoverable, so pay someone else to carry them. A cracked phone screen, a broken toaster, a rental car scratch — these are affordable, so carrying the risk yourself is cheaper than paying a premium plus the insurer's profit margin.
This is why extended warranties and product-protection plans are so profitable: they insure inconveniences at prices that assume you haven't done this arithmetic. The same rule explains deductibles — raising your deductible means self-insuring the small stuff and paying only for the catastrophic tail, which lowers your premium. Every insurance product priced to be profitable pays out less than it collects on average; you buy it anyway for the risks where 'on average' doesn't help you.
Consumer Reports has investigated extended warranties repeatedly over decades and reached a consistent conclusion: for most products they're a poor deal, because the typical product either fails inside the manufacturer's original warranty or lasts well past the extended coverage window, and average repair costs come in below the plan's price. Their reporting has also documented that retailers push these plans hard because the margins are extraordinary — service contracts have historically generated a large share of some electronics retailers' profits, far out of proportion to their share of revenue, precisely because most are never claimed. The economics are transparent once stated: the retailer is selling you a bet, they've priced the bet to win, and the thing being insured is something you could pay for out of pocket anyway.