Not really. The basic problem is "fractional reserve". Essentially an insurance company will only have about 5% of the money needed to pay out their policies (less in Europe, around 2.5%, and there's other variations across the world). (Even then significant amounts of that 5% would be either loans or shares, which are technically also loans. Most large insurers would go bankrupt if their risk assessments were off by 1%).
Since this is the exact thing that the double spending algorithm would check against this wouldn't be allowed, and therefore you can't have normal insurance in a blockchain world.