That government run health care would not eliminate denial of service is irrelevant to the tens of millions who have no service at all. It is also irrelevant to the wealthy who would still be able to contract private insurance to guarantee themselves rapid service (thereby relieving the public system of the burden of dealing with their `needs').
Rationing occurs in the current system - to oversimplify a bit - those who do not have a job which provides them with health insurance receive no care at all. Another way to say this is that the rationing in the current system is irrational and asystematic. Those with access receive, those without access do not.
Roughly speaking the US currently spends twice as much per capita on health care as do most Western European countries. The results in the US are inferior to those in Western Europe. There would be some cost associated with changing the system, but I don't see that you have argued convincingly that the cost would outweight the savings to be obtained by a well-regulated public system.
What would be wrong with a system in which doctors were paid less? There is no evidence that such a situation results in inferior service. On the contrary, many systems in which doctors are paid less (relative to the cost of life in the place in which they live) than they are in the US provide superior health care.
How are Canada and the U.K. `free-riding off the massive profits made in the American market"?This tendentious claim requires both explanation and defense. I suppose you mean that US drug companies finance their R&D with their obscene profits, and that the drugs sold in the UK and Canada would not exist were there not such obscene profits - or something to this effect. However, the profits are obscene precisely because they are profits, rather than money necessary to continue the business, and such a point of view seems to play down the role of UK and European drug companies. The government could itself mass produce certain essential drugs; or contract their production directly (in the same way it contracts the production of tanks). By the way, the basic research supporting the development of many of these drugs occurs in the context of perhaps the second most spectacular example of the success of public funding and public oversight - US research universities (the most spectacular example being the weapons industry).