In a free market economic system, providers of goods and services succeed by maximizing their profits through the low costs and high prices. That's a fine system as long as consumers have the option to refuse the service if they think the cost is too high. Unfortunately, you can't just refuse health care when you really need it. Even in situations where it's possible to do without, you're almost always heading toward a later, larger health crisis.
Here in the United States, our health care system is largely based on the profit motive. We've built a highly complex system of private and public providers, with insurance as a middle-man to manage financial risk. Some components of the system are non-profit, but they almost always do business with other portions of the system that do have a profit motive. Large portions of this system are motivated primarily by making money, conflicting with the aim of keeping people healthy. It may be possible to do both successfully in the short term, but eventually situations always come up where a decision has to be made between what's best for patients versus making the best profit.
Making the system work for most people has required the government to get heavily involved. There's tons of regulation, as well as programs like Medicare and Medicaid for those unable to pay the costs. With the Affordable Care Act, the government has also gotten involved in pushing consumers into the system, with penalties for the unwilling.
I'd much rather see a health care system that works more like the way those first-responder services are provided. For universally necessary services, the government should provide the whole system, including payment. There could still be private for-profit providers for non-essential services, like cosmetic surgery. (Similar to how private security companies exist, to draw another parallel to law enforcement.) That would cut out two huge flaws in the current system: the conflict of interest between profit and patient, and the inefficiency of the whole concept of health insurance (with no financial risk to the individual, there's no need to manage that risk with insurance).
Certainly this system wouldn't be perfect, but I believe it would be much simpler and more effective than what is currently in place. Of course, making such a change would require overcoming major resistance. The inefficiency of the current system makes a lot of money for a lot of people, and those interests are entrenched in the political system. The worst-case scenario of any possible change is trumpeted across the media (see: Death Panels), no matter how unlikely, and even honest politicians with good intentions find it hard to move forward.
I'm not sure how it would be possible to make these kinds of major changes in the US healthcare system, given the power and money with interest in the status quo. I'd certainly listen very carefully to any politician that came up with a plan, though.