Actually, insurance is very often positive expected value for the individual. He's paying the insurance company $n, which the company reinvests for even higher expected value, which is how the company makes a profit even when it's paying out to its customers slightly more than they put in. It's essentially the bank model.

I suppose that even when insurance is negative, its primary function is to buy protection against being shunted to $0 value. You're paying value to eliminate risk.

you're just renaming things here. the expected real (as opposed to nominal) value is still zero or negative. people don't run insurers out of the kindness of their hearts.

They compete with other insurance companies for customers. And the way to do that is to minimize the cost of insurance for a given payout. Which can push the expected value to go positive.

If a bank can pay you positive value (in the form of interest), an insurance company can as well.