Though note that an insurance may regardless be useful if you have self-control problems with regard to money. If you've paid your yearly insurance payment, the money is spent and will protect you for the rest of the year. If you instead put the money in a rainy day fund, there may be a constant temptation to dip into that fund even for things that aren't actual emergencies.

Of course, that money being permanently spent and not being available for other purposes does have its downsides, too.

I appreciate the extention on my thought process. It is very clear to me that since you have to pay an insurance premium buying insurance is necessarily a net loss. Buying insurance is very meaningful before a rainy day fund is filled up, if emergency financing methods are not available through a credit card or very trustworthy person and if the insurance contracts include other services, e.g. getting liabilities of the other party paid in case of their unwillingness to pay.

This is implicit in my phrasing

rare events with disastrous consequences

but made explicit by your post and will be included in the end report. Generally I come to the conclusion that buying insurance is a necessity unless you are perversely rich and even then there is some meaning found in insurance as even insurance companies themselves are insured. Just go for contracts with high co-pay to lower the exposition to the insurance premium which is basically just unnecessary bureucracy in case of small claims, as in the example of the $1000 dollar computer. For things in that price class I read an interesting sentence "if you can not afford to buy it twice, you can't afford it in the first place" alluding to self-insurance.