With a private company, if you are not satisfied with that particular company's service, you can always sign up with a competing insurance company.

Can you actually do that if you are covered as an employee of a firm that has set up a deal with an insurance company? Doesn't that mean you automatically dependent on that particular company?

That's a real question, not a rhetorical one. In principle it would be perfectly possible to have a system under which individuals woudl pick their own preferred insurance and the firm employing them would pick up the bill.