I didn't make that assumption at all. I assumed that we will get less value for our money the less competition and more regulation that there is. Current regulation already keeps us far from receiving optimal value for our money.
Healthcare doesn't make sense when viewed as a market economy.
First off, there is a potentially infinite demand for healthcare. (How much will you pay to live a little longer? As death approaches, the amount you will pay can be seen as an asymptote towards infinity. You have to be a particularly well balanced individual for this not to happen.)
Competing for actual finite resources (hospital beds, doctors, nurses, medications, the drafty-but-fashionable hospital-johnny), with a number of people who are going to die anyway, but are willing (if not able) to pay non-finite sums of money, clearly points us towards a conflict. The only conclusion is for the price of the finite resources to increase indefinitely.