There is/was a myth that Canada had the best health care system. Similarly that the US system was too expensive - 48 million Americans could not afford health care insurance. Thus Canada should not consider health care in the private sector. That is a myth. The uninsured in the US was just 17% of the US population. And the US has the best medical system. World wide people go to the US for treatment. Then one would expect high cost when one is getting the best service. 

So if Canada went for private sector health care, we could expect top service and about 17% of the population requiring help. That sounds pretty reasonable. And the constant bickering over health care cost would cease.

One other point. The private sector provides virtually all our needs and wants except health care. I cannot accept that health care in the private sector would be any different than other services. If it is more costly, so be it. You gets what you pay for.  Canada is a wealthy country.