My DH has life insurance through work. He also has critical illness / long term sickness cover through work. For his employer it is a low cost add on to the death in service which mitigates against the risk of them having to pay him long term sickness or negotiate his severance. I think this is fairly standard.
Public sector pension schemes also have provision for leaving work due to ill health.
I agree more people should be aware of what their employment offers and whether they need more. They should also be aware of what they are giving up / foregoing by not having these things through being self-employed / irregular employment.
However there are some odd comments on this thread.
If a person has T1 diabetes, HIV, cancer etc it may well be the case that they can get life insurance with exclusions. However they would rationally assume, as the insurance company does, that it will be some non-covered pre-existing condition which will kill them rather than the things they could get insurance for.
On intelligence the average is 100 with 50% of the population above and 50% below (standard bell curve). The MENSA population of 140 makes up about 2% at the top end and there is a similarly small cluster at the bottom end who would not be in a position to make independent financial decisions and are therefore not part of the insurance market. There is not a subset of 20% "tall" boffins skewing the average upwards for the rest. In fact the vast majority of the population are clustered slightly above and slightly below 100.
It is an entirely different question whether the insurance industry is transparent enough to allow averagely intelligent people to make informed decisions around purchasing insurance (PPI, low cost endowments, Equitable Life etc, etc, etc suggest not). If it is not then it is up to Society / Government to step in either via compulsory insurance (cars) or social safety net (NI plus welfare). Blaming people and making an unfortunate few bare the cost to frighten the rest does not look to be a great way to regulate the market or protect the individual taxpayer.