The problem is that a badly designed health care system will have rotten incentives. Think of it this way, suppose a law was passed making the price of lobster 1/100th its current price. The obvious result is that there would be far fewer lobsters on the shelves. People would purchase the existing inventory, and at these low prices lobster fishermen would switch to other more profitable catches. We saw this kind of thing with the price controls during the past oil crises. And we see the same thing in Canada with one huge difference: unlike lobster there aren't many substitutes for health care services.
As with the lobster example, there is a shortage of both nurses and doctors in Canada. This should be obvious. Where is one place that the government can control costs? Doctor and nurse salaries. Fix those at a fairly low level and the rate of increase and you can help control costs. Since doctors and nurses are almost all highly intelligent and motivated people they will see that they can get more for their work in other occupations or in other countries. So you end up with a shortage of doctors and nurses. The exact same logic applies to hospitals, MRIs, and other things as well.
On top of it, I'd argue that there are in effect uninsured people in Canada and lots of them. What is the benefit if you have government insurance if you still have to wait 10 months to get an MRI, and 18 months to get the procedure done? For 18 months you don't have health care that you need. In effect you have no insurance as you sit there in pain and missing out on large portion of your life.