With insurance, the expected worth for you has to be negative, otherwise how would insurance companies even survive? The value of insurance is not reducing the average loss, but reducing the risk. For example you lose $10 at a probability of 100% instead of $1000 at a probability of 0.5% (that is losing $5 on average). If you look at the probability distribution of your losses, you are not moving it to the left (lower average), you're just making the distribution narrower, that is you reduce the chance that you lose large amounts.
In summary, if losing $25k is no big deal to you, you can on average save money by not buying insurance. If losing $25k is life changing, you should pay some money to reduce the risk.
Insurance also has quite a bit more weight to toss around than you do. So, you’re comparing cost to them vs cost to you which can be very different numbers.
Health insurance negotiators for example often save you more money than their profit margins. It’s dead weight to society but personally it’s a net gain.
> What about the risk of your insurance company going bankrupt?
For most insurance ordinary people would have, except possibly life insurance [1], coverage comes into effect fairly soon after you pay your premium. If your current insurance company is showing any signs of insolvency, you should be able to switch to someone else and get covered.
If there were no warning signs that your insurance company is in trouble and they unexpectedly go bankrupt, but at a time when you don't need to make a claim, you can quickly switch to someone else.
If they go bankrupt and you are making a claim, it should be covered by your state's guarantee fund. Insurance is a regulated industry, regulated by the states. Part of that regulation includes the state establishing a fund paid for by the insurance companies that is essentially insurance that the insurance companies can pay claims.
If you pick a large, diverse insurance company, probably the only real risk that they might unexpectedly go bankrupt at a time when you need to make a claim, and the state guarantee fund might not be able to cover it, would be during some major widespread disaster that causes severe damage over a wide area. You might be screwed then, although there will probably be some kind of Federal disaster recovery aid available then.
[1] I have never looked into details of life insurance so am not sure how that works.
AIG cyber policies provide dns filtering appliances customers are required to put in front of their networks. Supposedly works really well for them. Does anyone know if Zurich did the same?
In summary, if losing $25k is no big deal to you, you can on average save money by not buying insurance. If losing $25k is life changing, you should pay some money to reduce the risk.