It could be across a pool of investors, as you describe in the spice-trading example. Nobody wants to self-insure because of the chance of a huge catastrophe taking out their ship and netting them a huge loss and likely a lifetime of debt.
It could be across a pool of investors, as I describe in the health-insurance example. Nobody wants to self-insure because of the chance of a huge catastrophe putting them in the ER and netting them a huge loss and likely a lifetime of debt.
The reason we leave it to big organizations currently is because they have the resources (data, underwriters) to accurately asses and price risk. They charge a fee to do this. They are allowed a certain amount of extortionate leeway due to government regulation mandating certain minimum amounts of insurance, which you allude to in arguing with companies for reduced rates.
Things we could do to make the system better:
1) Reduce barriers of entry for doctors
2) Stop prescribing unnecessary treatments/prescriptions
3) Better education regarding health choices
4) More taxes/tradeable permit system for companies that pollute bodies or the environment (McDonalds, ADM, Dow Chemical, Bayer)
I would argue the word has been bent and beaten far out of its original shape into something close to what you're talking about, especially in health. It's not insurance as much as assurance. You don't pay in early in life to get the expected value later in life. That would be insurance. You fight to try and get more than you deserve when you're above the life expectancy, if you're good at paperwork. If you're bad at paperwork or a smoker, you're the one whose early death frees the medical resources and insurance money needed to pay for the one who's good at paperwork, less a fee for the broker and all the rest.
In this second meaning of "insurance" you're right, the point is totally defeated because nobody will want to "insure" a sickly old man's health just as nobody in their right mind will write fire insurance for a cigarette.