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 insuranc

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.