Earlier quoted context omitted.
> Insurance brings other benefits that improve your life. What other benefits besides the money that covers the losses?
Hedging risk. This is often a hard concept for people to grasp: there is value to hedging risk. It (generally) cannot be turned into money. There is extrinsic value to reducing risk.
Same with insuring some painting let's say. You can get enough money to buy a different painting, but the risk of losing that particular painting is still there. If it is a unique painting and it gets lost, how are they going to repair the non-monetary value of it? They can't.
Hedging the risk of being shot by wearing armour sounds like actual hedging. Buying insurance against being shot sounds like just betting. The non-money part is exactly the difference, and it is missing in insurance.