Comment by rlpb

Another advantage of insurance is that if your insurer is responsible for the rectification then you benefit from collective bargaining at a time when you may be unable to do so yourself.

For example, if my car breaks down in the middle of nowhere at 3am, I expect I'll end up paying far more for recovery were I self-insured than a breakdown insurer will.

I think the article you linked is flawed because it presents a mathematical solution without taking this into account.