Comment by mlinhares
I haven't been in a car accident for 15 years, not even fender benders, that doesn't mean I shouldn't take insurance.
As someone from a random developing nation car accidents deliver crippling debt and destroy lives there frequently because insurance is not mandatory.
The developing nation blindly ignore the externalities of not having insurance (instead of spreading the cost throughout society, only a few people bear the brunt of it, usually the ones least equipped to handle it), so your example is great only if you assume its fine to continue to beat down the poor. There's a reason developed nations have developed such "red tape" and the anti-vaccine movement here in the US is finding out what happens when the red tape is removed.
It comes down to the amortized cost of insurance vs amortized cost of not. Say nothing about how incentives get fucked all to hell by breaking things across many parties (principal agent problem) and the money distorts things.
And this isn't just insurance. Just because someone who work is being made for by law or by rule says that their work output reduces the failure rate from X to Y doesn't mean that the cost of their work when applied to everything isn't a massive loss compared to just not paying for that and cleaning up the mess X times instead of Y times.
You can appeal to emotion all you want but it's a very simple calculation. Heck, health insurance (in the US) serves a pretty obvious counterpoint.