Part of the problem with for-profit healthcare, is that as a consumer you often don't have a choice in your demand. That is, if you don't buy what they are selling you, then you could die. It hard to find good competition when the clock is ticking and you really really need what they are selling.
To put it another way, if you have a product that the public, literally, can not live without, why would you ever sacrifice profits in order to make sure it is affordable to everyone?
The laws of capitalism would say that you need to increase what you charge in order to maximize profits, not availability. If maximizing profits means out-pricing 10% of the public, then that is what you do, and that is exactly where we ended up in this country.
I don't think its something that can work on a national level here in the U.S. Not just because of the system, itself, but because the consumers can't handle it. Too often people don't go to the doctor and act like a customer, they see the doctor as some kind of infallible authority. And the People don't seem to want to take matters into their own hands.
The rampant dogma against socialism on the political right is what is preventing us from getting universal, single payer healthcare.