This is wrong and the reason you are confused about the argument. If insurance is priced fairly all parties benefit utility wise. It's true that the buyer has negative expected value money wise and the seller positive one but as the utility function is concave both parties benefit. The important thing is to be able to see value in insurance. Once you are able to see it you will understand why it's worth a premium.

One natural question is why the insurer can afford to sell the insurance and not lose expected utility. The answer is that the insurer has a bigger bankroll and the utility curve is flatter for them than it is for the buyer. That's why they can offer a lower premium than an individual in similar position to the buyer would be.

This is obviously the insurer's goal, but in practice competition and relaxing underwriting standards to win business means that many insurance companies do not turn an underwriting profit (the buyer winds up with a positive expected value). But premiums are paid up front and payouts to policy holders do not occur until later, and the insurer can invest the "float" in the meantime, so they still make money.

Obviously the customer could have taken the premiums and invested them themselves, but that also takes time and effort, and may come with risk itself. It is not obvious that insurance is a bad deal even ignoring arguments about the concave nature of the utility of money.

It is just the same can’t find any logical argument that makes it different in any post. Feels like everyone is trying to justify it