Unless you can sustain a $100,000-$300,000 loss before you have have paid into the insurance pool more than that amount, it makes sense. If you had gobs of money, then it wouldn't make sense for you to have insurance. (preconditioned on insurance being a profitable business, etc.)
By analogy - if a person thinks "spending $5 has no impact on my life, but winning $10M will", is that really any different from our justification of insurance? (I agree with you - thats the same way I view insurance. Yet I view lottery tickets as silly, but I can't clearly articulate why).
The cumulative impact of a lifetime of spending $5 per week is much less than winning a lottery. Most people can sustain a $5 per week hit, especially if they get the mental benefits described by the parent article.
There are better things to spend $5 on, but it's not a huge deal either way - as long as you stay out of the addictive/compulsive zone.
The losses covered by insurance are very impactful. Most people can't sustain the massive financial hit that comes from, say, their house burning down. It can make sense to lessen their day-to-day quality of life by spending money on insurance, to guard against that massive downside risk.
Hm. Most people collect on insurance for very-sustainable costs - drug benefits, dental for checkups, routine visits to the doctor. Where do those fit into this argument?
Personally, I would like insurance that pays only for large expenses. I know its a sucker game to pay insurance; since the insurance companies profit I must be losing. But 'group insurance' is not something I can change.
Insurance significantly reduces the possible (or significantly likely) variance in a persons financial well-being. This comes at a cost in total wealth that is worth while because it brings the chance that one would vary into territory where the money one has is not enough for basic utility. Insurance on the other hand increases the variance (meaning the slight increase in expected value comes at a cost) at the other end of the spread in a way that does not guarantee any kind of minimal utility. Minimal utility is more important than huge potential diminished returns.
You also have to consider loss aversion which is a well known psychological phenomenon[0]. In a sentence, people fee when tend to strongly prefer avoiding losses to acquiring gains.
