I am unsure of how your healthcare system works. Is it possible to pay for more timely service from a private hospital or private doctor?
If it is possible but not feasible because of cost, then an American, speaking practically, experiences the same thing. Not enough money to pay for medical service. However there is an important difference.
An American must pay something out of pocket. The financial burden may lead to bankruptcy and ultimately no medical care at all. I've noticed that you did not raise concerns about bankruptcy but instead your concern was over slow medical service.
You cannot pay to "jump the queue" in Canada if the health care procedure is covered by public health insurance which includes most things you'd expect a doctor to do or prescribe.
You can only pay to jump the queue by leaving the country, such as going to the United States or India for medical treatment.
It's different in new Zealand. If you don't like the waiting list you can have private insuanace or pay yourself for a private hospital. We did this when my wife had a melanoma. Waiting list was 3 months (non urgent) so we went private. It cost $4000 (operating room, surgeon, nurses etc).
If it is possible but not feasible because of cost, then an American, speaking practically, experiences the same thing. Not enough money to pay for medical service. However there is an important difference.
An American must pay something out of pocket. The financial burden may lead to bankruptcy and ultimately no medical care at all. I've noticed that you did not raise concerns about bankruptcy but instead your concern was over slow medical service.