I don’t know a health care system where you can’t buy secondary insurance on top of national health care.
The reason is because physicians are banned from treating patients in the public system and private system. If they choose to treat private patients, they can't work in the public system. With such a small private system, that's not sustainable.
In addition, private hospitals/clinics can't offer certain procedures. MRIs are allowed in some provinces, but the list isn't very long.
Basically Canada is not interested in having any private healthcare system because then it would be "2 tier". They prefer everyone go to the same system.
The reason was a wave of “extra billing” that had swept Canadian healthcare in the 1970s. Canadian patients were increasingly being hit with user fees and copays that were gradually chipping away at the supposed universality of Canadian healthcare."
Basically, private doctors wanted to be able to also bill the public system and any additional cost the patient is required to pay. That went against the idea that "healthcare should not be purchased".
[1]https://www.capitaldaily.ca/news/private-two-tier-healthcare...