The EV of insurance is negative, in the sense that the expected money that one can expect to get out of insurance is less than the premium.

Insurance is for catastrophic losses. I don't pay for insurance to make a profit, I make it to avoid the large tail loss of having the house destroyed and having to pay the value of the mortgage to the bank.

No, it's still very valuable since I'll never have to pay out of pocket for that million-dollar incident. The point isn't to save money, it's to distribute the incident payments over a long term.

These kinds of questions are a little mind-binding. Insurance is a financial services business. If the net EV of insurance was positive, how could any insurer remain solvent?

Generally insurance premiums are invested into relatively safe assets, like bonds, which yield quite a bit right now.