But you are only able to hedge the money part of the risk. Life insurance does not bring anyone back, and health insurance only repairs your health as much as can be done with money. You can't insure against incurable diseases, as in the risk remains. You will just get some money to hopefully feel better, or for your children.
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.
Yes, you are hedging against financial loss. Most of the other stuff you describe, e.g. sentimental value of one painting vs another, are irrelevant to insurance. You pay a (relatively) small amount to eliminate the risk or mitigate the effect of getting a massive (specifically financial) loss.
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.