An article by D. Eric Schansberg on the topic of "Envisioning a Free Market in Health Care" has an interesting table showing for various time periods the rate of "excess cost growth" in health care, meaning the differential between the average annual inflation rate in health care and the average inflation rate of all consumer prices. The numbers:
His point is that once upon a time, before health insurance became widespread, health care prices did not climb more rapidly than other prices. I am actually a bit surprised that the numbers are so striking. But it makes sense.
Keep in mind, though, that even if we had not expanded third-party payments, health care spending probably would have risen faster than other spending. That is, I think that the inflation-adjusted demand for health care has been on a long upward trend.