The point (in theory) is that in efficient markets you can choose between different companies offering a product/service and that competition drives down prices / costs. The healthcare market in the US is very much not a competitive market (in part due to transparency issues which this is trying to address, in part because of the perverse incentives in the health insurance system).

It's not so easy to have a competitive marketplace for government services (though I would not be surprised if the US saw the emergence of private police forces now, for those parents who actually want police officers that have a duty to protect their kids...)