1. If you choose not to take out an insurance policy, and instead save the money yourself, you will not have the lump sum immediately available to cover catastrophe. Whereas as soon as you start paying insurance premiums you are covered.
2. The payout you receive when you make an insurance claim does not just come from the premiums you have personally paid. In fact, for a rare event, the size of the payout likely exceed the total cost of all premiums you could pay over your entire lifetime. This is because the risk is pooled over all customers, and not all customers will make claims.
Neither of the above 2 points become any less relevant as the insurance premiums become more and more accurately priced.