In the past, more hospitals were owned and operated by municipalities and churches and were run as non-profit, but most hospitals today are owned and operated by private corporations, and they have shareholders to satisfy and executives to pay. Most health insurance companies in the US are also privately run and for-profit with their own set of executives to pay and shareholders to satisfy. Worse yet, anti-trust laws, especially with health insurance, do not apply, the by-product of an aborted attempt at health care reform back in the 1930s. The compromise was that states and not the fed would regulate the market against anti-trust activity, but states largely reneged on that deal but kept the exemption.
If you look at it from a market-based perspective, both hospitals and health insurance companies are good examples of markets where competition is very weak or non-existent. With lax competition comes the temptation to implicitly collude on pricing structures with health insurance premiums, and if you are, for instance, a gun-shot victim, you don't have time to pick and choose which hospital you're going to want based on pricing. You simply want to go to the nearest hospital for service.
The health care system in the United States is a good example of everybody wanting a cut and nobody listening to the patient. Greed has come before the patient, and I do not see the system changing regardless if you required everybody to participate. As long as price-control mechanisms remain trivial, it'll just get worse.