When the idea of insurance started, it was usually a small group of people getting together to take away some uncertainty so they get on with their lives. Life has a habit of throwing curve balls. I don't think it is malicious though. We just start to get down on ourselves about being unlucky because we spot patterns in things that aren't there. We don't have a good understanding of what random means. If a sequence of coins is flicked and two outcomes produced are HHHHHHHH and HTHTTHTH, we will believe that the second one is more random. They are both equally likely. The Gambler's fallacy is what keeps us coming back to roulette tables, or believing a lucky run is showing more skill than just luck. We love a good story.
Insurance should ideally help take away the noise. If a group of 10 people are sending ships from England to New England and one is likely to sink on each trip, they would rather group together and take a small hit for sure, than risk everything. This is why a lot of insurance companies were Mutuals - i.e. a group of people mutually sharing the risk. That is where Old Mutual comes from.
One of the risks with insurance is a thing called Moral Hazard. It is not only toddlers that respond to incentives. If you know you are insured, your behaviour tends to change. Especially if the risk event (i.e. a ball flying into the TV) results in something you are actually pleased about (i.e. a new TV).
Insurance benefits from 'The Law of Large Numbers'. Flick a coin once and you would be very unsure of what the result would be. Flick it a million times and I would be willing to place a bet of my entire life savings that there would be more than 40% of each option (if the coin was fair). The result will be incredibly close to 50/50. The true underlying probabilities. No noise. Noise comes out in the wash.
So Insurance Companies benefit from being bigger as they are able to predict things better. The flip side is that this is less a case of 10 buddies getting together to cover each others ships. The oversight of banter over a few post journey beers disappears. Behaviour starts to change.
Instead of getting insurance that makes things that go wrong hurt less, we want them to not hurt at all. We want a lost phone to mean an upgrade. All this means insurance becomes more expensive. We aren't just paying for the losses we would have incurred, we are paying for sweets and Disney plasters to make the hurt go away.
The only way to avoid not paying for this is to only insure the things you need to. And to accept the bumps in the road without turning them into mountains. Don't remember to insure your television and your car, but forget to get insurance in case you get disabled. Bumps v Mountains.
If you want a life with no bumps, don't do anything worthwhile. Bumps add flavour. Mountains add perspective.