You absolutely can do this. For many of the minor issues covered by insurance, like dental visits for health insurance or a small water leak on your home insurance, this is probably fine.
Consider, however, the major catastrophic risks that are covered by your insurance. What if your house burns down and you lose everything? What if you get cancer, or heart failure, or some other very serious illness? Insurance is there because most of us don’t have the savings necessary to rebuild if our whole life gets pulled out from under us.
Insurance companies do plan not to spend more money helping people than they take in through their premiums, so you’re right that in very large numbers, most people could do what you’re suggesting and be fine. But the insurance doesn’t exist to cover small ordinary expenses; it exists to cover life-changing catastrophes. The few people who suffer those, won’t have enough in their savings account to cover them.
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