A Rand study found that even when you give people completely free access to healthcare, there is no significant improvement in outcomes:

"If you remember only one medical study, it should be the RAND health insurance experiment, where from 1974 to 1982 the US government spent $50 million to randomly assign 7700 people in six US cities to three to five years each of either free or not free medicine, provided by the same set of doctors. The plan was to compare five measures of general health, and also 23 physiologic health measures. From their expanded 1983 New England Journal of Medicine article:
...
The bottom line is that thousands of people randomly given free medicine in the late 1970s consumed 30-40% more medical services, paid one more "restricted activity day" per year to deal with the medical system, but were not noticeably healthier! So unless the marginal value of medicine has changed in the last thirty years, if you would not pay for medicine out of your own pocket, then don’t bother to go when others offer to pay; on average such medicine is as likely to hurt as to help."

http://www.overcomingbias.com/2007/05/rand_health_ins.html