Let me give an example of how private system works (e.g. in Britain). For cataract surgery, in our area there is a waiting list of four weeks. So once the ophthalmologist determines that you need the surgery, you will be scheduled four weeks from now.
But let us say that you want it done earlier. Then in Britain, you could go to a private hospital and get it scheduled much earlier, perhaps the very next day. Then if you had private insurance say, with BUPA (when I lived in UK, BUPA was the biggest private insurance company), then BUPA would pay for it (you may have to copay depending upon your contract with BUPA). If you don’t have private insurance, you could pay out of your own pocket if you could afford it(and if you want to do it the very next day).
This would be an alternative to getting it done four weeks later for free with NHS. This is how private medicine works. Most developed countries have such an alternative, Canada doesn’t. In Canada, you cannot buy insurance for cataract surgery, since it is covered by the government. You probably wouldn’t be able to find a doctor who would do the surgery for you, even if you are willing to pay out of your own pocket. For the doctor to do that, he would have to completely opt out of health plan, never charge anything to government. That is not a realistic option for the doctor. Your only option would be to go to USA and get it done.
So the alternative that is available in most developed countries is not available in Canada. In that respect, Canada is an oddball.