Competition is best, economists often claim. Except when it is not, for example in the case of natural monopolies, where the duplication of infrastructure is wasteful. THe case can also be made that competition is not as good as one would think in the insurance industry
Giuseppe de Feo and Jean Hindriks explain that adverse selection has worse consequences under competition. Indeed, in a monopoly, the insurance company can make profits on some products which allows to cross-subsidize others. With competition. profits are driven to a minimum, and cross-subsidization is minimal. This is important because cross-subsidies allows to relax the incentive constraint. This provides better coverage for high risks, but lowers participation among low risks.
One aspect that was not mentioned in the paper is that monopolistic insurers, because they have a larger market share, are better able to diversify the individual risk of the insureds. Observationally, this makes them closer to risk-neutral, and thus allows them to offer lower premiums, every else being equal. Of course, they could use their monopoly power to raise premiums, but with smart regulation or threats to entry, this can be prevented and the full social benefit can be obtained.