People can make good decisions, but one health care provider (e.g. the government, in most countries) can provide health care and purchase supplies more efficiently than individuals can.
Specifically, the American system is flawed because 'shopping around' between different providers whose sole purpose for existing is to make and maximize profits just results in you picking someone who's taking the least advantage of you. A single payer, for example in Canada, you go to any doctor, clinic, hospital, pharmacy, etc. and you get the thing. The health authority pays a fixed amount to the provider (and they make a good living, make no mistake), and the health authority attempts to maximize the value it gets from every dollar without compromising patient care, and following the mandate that everyone should have the same access to care.
The limited research so far seems to show people generally make good decisions when given money without stipulation, and the idea we need to tell them how to spend their money "despite themselves" is probably very misguided.
Of course, more research is needed, which is exactly what the YCombinator program is planning to do.