Theoretically, it could produce competition between the insurance companies. Sure, you have to buy insurance from someone, but do you want to buy it from the company which has more doctors close to where you live, or the one which pays for PSA blood tests? Maybe one company only pays for you to visit your GP when you're sick, while another decides that they can save money by encouraging you to get regular checkups and catch problems before they become more serious.

I don't know if this sort of story actually plays out -- I live in a country where the only way to get better health care is to move to a different province -- but it doesn't seem completely implausible.