You're right that they do have an interest, but I think it is wrong to go as far as if the expected value of the loss is more than the premium then one shouldn'

You're right that they do have an interest, but I think it is wrong to go as far as if the expected value of the loss is more than the premium then one shouldn't buy insurance. Consider a risk of losing $200 with probability 5% on an asset of $2000. The expected value of the loss is $10. So under your argument, if the insurance company charges over $10, it's worth it to self-insure. But what does self-insure actually mean? I assume it means keep $200 lying around. If you only keep $10 around then you won't have the money to actually fix the problem, and convert a loss of $200 (say, repair costs) to a loss of $2000. Under my values here it would take over 20 years' of premiums to build up what you would need to save to self-insure! As a consumer, I pay a premium (literally) to get rid of the risk and cap my expenditures. So in my example, there is some price between $10 and $200 where the insurance company can profit and I still come out ahead because I can take $200-P and do something else with it. Of course, you are still correct that within the $10 to $200 do have an interest in making you believe that the value of the insurance is on the higher end of the range than the lower.