Assuming that insurance is correctly priced, buying a policy in any form is negative expected value. The companies that write such policies would slowly bleed dry if that wasn't the case. However, that's irrelevant unless you have the bankroll to withstand tail risk. Given that most people don't, as a society, you pretty much have to make things like auto liability insurance compulsory. If you're a "good driver," as…
This would only be true if the value of money was linear.
The value of money is not linear.
A 10% chance of a 1000$ loss can be far more harmful than a 100% chance of a 100$ loss, especially at low income.