- Rare, but predictable in a statistical sense, ie x% of people will claim for y amount, and actuarial tables say so.
- Expensive to compensate. This is why we need to spread the risk.
- Where's it's hard to separate risk levels of different people. If not you get adverse selection, where the average cost discourages the safer people, leaving the less safe.
With the recent revelations about brain damage from tackle football, the actuaries will rightly decide that their old tables are systematically biased. More people will be allowed to claim that initially believed from the old evidence. Furthermore, you can't just up the premium to compensate, you don't know how bad it might get. There was that one study of old NFL players' brain that concluded all of them (!) had damage to their brains. You also don't have any idea what the courts will award, so you really have no clue how much to ask for.
You also have to ask whether general health insurance will start asking people whether they play football. (I'm not familiar with the US system). Much like smoking, it might turn out to be a predictable high risk group, so that people in it will have to pay prohibitively more for coverage, or not get covered at all.
So if all the youth players can't get insurance, you have to wonder what will happen to the professional game.
Perhaps there's some major rule change necessary. I'm not sure how I'd change it to be similar but safer, something about the game seems to require tackling to be football.