It does seem like it's time to stop letting this "industry" profit off the misfortune of its customers. Making all of these a public service instead of private industry makes sense at this point.
Ironically they don't profit off the misfortunate customers. Those ones typically get back more than their premiums.
They profit off the fortunate customers, those who have no need to claim from insurance.
The profit margins on insurance are usually pretty slim. Insurance companies are generally not well differentiated from one another, so they have few avenues to compete other than on price. A state-run insurance plan also has to operate at a profit/surplus or else it will have to be subsidized by the taxpayers. The effect is the same either way.