Anytime people are removed from the cost of a thing, the price goes up. Housing, education, healthcare. Even buying groceries people spend more than twice as much with a credit card vs cash.
If removing something from the market led directly to massively inflated costs, we'd expect those systems to be the most expensive, but that's just not true.
Elective services like dermatology and cosmetic have managed to keep prices in line with what people can afford to pay out of pocket.
The other inflators in the US has been emergency room visits for people with no coverage at all, which are 10x more expensive than simply visiting a primary care physician. Plans pushing for funded HSAs would totally eliminate this problem as even the poorest people would have a reason to go where they could get more cost effective care.
I want to mention one very specific thing about this though, these services are very different than other medical services not just because of the difference in insurance markets, but also because unlike many, many procedures they are elective.
The health market is so interesting because one of the normal recourses available to market participants normally, that is doing without, is not available in certain situations int he health market.
> The war itself played a major role in the growth of health insurance, according to a March 2002 history of health insurance benefits from the Employee Benefit Research Institute, a think tank that examines employment-based benefits. Wages had been frozen by the National War Labor Board amid a shortage of workers as many potential employees went off to fight in the war. Employers sought to get around the wage controls in order to attract scarce workers. Providing them health insurance was one way to do that, EBRI said.
> "During this time, employers petitioned, and were granted to have benefits, particularly health benefits, not be considered part of wages," Stephen Blakely, the director of communications and managing editor at EBRI, told us. "Congress agreed to exempt health insurance benefits from taxation."
http://www.politifact.com/virginia/statements/2014/oct/30/ja...
https://en.m.wikipedia.org/wiki/Health_insurance_in_the_Unit...
See History
Nobody is saying unions are perfect, but corporations and plutocrats aren't going anywhere, and labor is the only countervailing force.