I think the biggest reason health insurance is provided by the employer, rather than bought by individuals is adverse selection.
Simplistically: people who are more likely to suffer an illness (e.g., people with pre-existing conditions) will buy more insurance, and people who think they'll be healthy (e.g., younger people) will buy less. This drives up the amount of payments per insured, which drives up price, which further drives healthy people not to insure.
That's why you want health insurance purchase to be independent of risk of illness, which is (at least somewhat) what the employer-provided insurance does.
This is probably also the main reason state-provided health insurance might be a good idea.
Banerjee's and Duflo's 'Poor Economics' gives you a more detailed and nuanced explanation pp. 147-151. Great reading throughout.