To front-run the complaints, "same quality" does depend on specifics. The USA really does lead the world in breast cancer and diabetes treatment. It is in the middle or back of the pack at nearly everything else, though, including cost, which is >double, even for treatments without quality to match. Most people would not pay >double for this if they had a choice.
They don't. They offer different services at lower overall cost. Cancer survival rates are the highest in the U.S., mostly because people don't like to die, and the U.S. is (by and large) stinking rich. Here in Ontario, I got a double ear infection (from swimming in lake Erie a few days before symptoms started), and was prescribed a combination eardrop. I'm under 25, and do not have private supplemental insurance, but I expected something like this to be covered by OHIP+; turns out they decide not to cover it unless you've been experiencing symptoms for almost a full month.
I ended up paying (it wasn't so bad, honestly) out of pocket for it, since my jaw was almost completely seized up at that point.
Now, you expect something like this to be covered, but these particular drops (I guess the doctor assumed I had supplemental insurance, or knew I would prefer this product [it worked very well and was easy to administer]) are not covered except as a last resort.
In the U.S. system, the majority of people pay for the privilege of at least partial coverage of more convenient/effective (but more expensive) medical products and services. The U.S. market produces high demand for medical products and services, and by-and-large has more disposable income, so prices can be higher.