Einherjar,
I believe the effect you describe may occur, but not to the extent you suggest.
The best solution by far is a free market for everyone. However in nearly all western countries, the U.S, included, the free market for pharmaceuticals and medical treatment generally is highly distorted by government intervention. It happens that this distortion is a good deal less in the U.S., compared to Canada and Europe.
Change in Europe and Canada does not seem likely, despite the stagnation in service quality they are all experiencing. This problem is nested within a larger one involving the continued ability of these nations to sustain their rather expensive social welfare systems in the face of ageing and declining populations and low economic growth. So far the internal political resistence to change is very strong.
Meanwhile the U.S. continues to tinker with a relatively free market in ways that tend more to complicate its operation than to meaningfully improve access to the least served elements of the society. The remaining free market aspects of our system do a lot to support the development of new techniques and drugs for the world - as has already been noted here. Certainly if the U.S. were to socialize its system to the extent of other western nations, the future progress of medical treatment would end up with all the creativity, inventiveness and agile response to new developments for which government bureaucracies are so well noted.