A "market" is a place where a user can purchase goods or services. In healthcare, who is the user? Not the patient. The patient can't order her own tests. The patient doesn't even pay for the services. Some third party pays, such as insurance or Medicare. The recipient of the funds, the seller, is the healthcare provider. The reality is that the "market" in healthcare has one party as both the buyer and the seller -the healthcare provider himself. The doctor determines the services that will be rendered and then orders those services to be bought from himself or his associates. Rest assured, there is no "market" in healthcare.
The claim from the other side for "universal coverage" is a red herring. Is universal auto insurance an effective mechanism for keeping down the cost charged by the collision repair shop? No. One has nothing to do with the other. Insurance is simply a transfer mechanism. It's a way to take money from group A (those buying the insurance) and giving it to group B (the providers of healthcare services). Note that we've already posited that healthcare services providers are both sellers and buyers of their own goods. It's quite a perverse system.
All the answers on the table today ignore these simple facts, and in so doing exacerbate the problem. They're simply missing the boat.