Marc, I grew up in Poland. My political views crystallized in 1970s under the strong influence of Marxism-Leninism, and my observations of its practical implementations. By the way, it included the kind of health care system that Cheney advocates for.
Many years later, some of my American friends pointed me to writings of Ayn Rand. I agree with her that accepting individual’s egoistic goals, as the most basic ones, is the simplest and most moral social contract. Under assumption that people satisfy their goals with money they earn not money they extort from others; as Cheney demands.
Consequently, you are incorrect claiming that our system cost so much due to a few oligopolies abusing the free market. It is exactly the opposite. We do not have the free market in healthcare anymore. We already have a unified single buyer as you ask for, it is Medicare. Whatever lobbyist from these few oligopolies negotiate with Medicare, the whole health care industry follows, and this is what you and everybody else pay.
Today, the free market operating businesses figured it out how to sell to poor people as Cheney many basic products and services. If health care would operate in the same way, she would be able to find an affordable health insurance satisfying her needs; much better than she can have it now.