I think that for the serious cases of unexpected misfortunes, an insurance is a compressor where all population events are the whole signal and individuals make

I think that for the serious cases of unexpected misfortunes, an insurance is a compressor where all population events are the whole signal and individuals make the peaks (well sometimes many a person are in the same event): For the subset of people that would need an insurance without knowledge that could prevent that, the consequences should be distributed among all people. (Sure, there are exceptions if taking too big a risk.) And personally I feel most medical issues and school should be paid by the state as it would be too unfortunate if an individual should face alone the consequences -- and possibly couldn't afford for an insurance, or is likely not to buy it because has other monetary issues.