Let's not even go there. Let's look at a less regulated medical field of dentistry. Dentistry is relatively cheap and available because there is, while still heavily regulated, a market. I.e. you can call a doctor's office and get a quote for whatever procedures you want. Don't tell me that someone with acute toothache is in a superior bargaining position than someone with, say, elevated blood pressure.

So the market works pretty well when you don't over regulate it. I somehow doubt that bringing even more regulation in form of single payer will suddenly fix anything.