First of all: the payout you get from insurance does not come only from the premiums you personally pay. If you make a claim, your expenses are covered by the pool of money of all customers, even those that do not make any claims.
Second of all: when you take out an insurance policy and pay your first premium, you are immediately covered. If you are "self insuring" by setting aside the same amount monthly, it will take you a long time to even begin to accumulate enough funds to cover yourself in case of catastrophe. (And due to the first point, you may never reach that point.)
Finally, yes, of course, there is no need to take out an insurance policy for a risk that you can afford to pay out-of-pocket. It's like how if you have the cash to pay for a house, there is no need to take out a mortgage.
