Of course insurance companies are first and foremost trying to maximize their profits by charging everyone just slightly more than their expected payouts . That also means that their profits go up when they get better at modeling someone's risk profile and then charge them more. The whole business model of insurance depends on treating people differently, even if they are different due to no fault of their own.
 corollary: if you have enough money, you shouldn't buy insurance (expected loss), but insurance companies (expected profit)
The Expected loss with insurance is higher than without for two reasons:
* The insurance company must make a profit
* You are much more likely to go bankrupt than the insurance company. Bankruptcy limits the payout.
The only time you should take insurance is when you know something the insurance company doesn't. For example, you know how very dangerous your house electrics are, while they don't. Take that thinking too far and it's called "insurance fraud" though.