The problem rather is the insane amount of red tape involved if you want to set up your own health insurance company. Thus hardly any competition for the established player arises.
The result is what any arbitrary textbook about economy will tell you: if there are large barriers to entry into a market (i.e. the opposite of "free market"), the customer won't get the positive consequences of a free market, but instead oligopolies will form - with their negative consequences.
The result is what any arbitrary textbook about economy will tell you: if there are large barriers to entry into a market (i.e. the opposite of "free market"), the customer won't get the positive consequences of a free market, but instead oligopolies will form - with their negative consequences.