At least here in quebec, the private system is not allowed to provide a lot of services and cannot provide much more than basic consultation, cosmetic surgery or treatments that are more or less arbitrarily allowed by the public insurance system. Tons of people went to the state when the public system basically stopped treating anything they didn't deem to be essential for almost a year back in 2020. I know tons of US hospitals did the same, but some didn't so you at least had a choice.
Here, once the government decided that your disease, surgery or therapy wasn't "essential" you couldn't do anything at all because the private system can't do most them either. Both of my parents are nurses & according to them at one point their hospitals were almost entirely empty, but because of that arbitrary you still couldn't access most non-urgent care which was very frustrating for them.
Chaoulli v Quebec (AG) [2005] 1 S.C.R. 791, 2005 SCC 35, was a decision by the Supreme Court of Canada of which the Court ruled that the Quebec Health Insurance Act and the Hospital Insurance Act prohibiting private medical insurance in the face of long wait times violated the Quebec Charter of Human Rights and Freedoms.
Here, once the government decided that your disease, surgery or therapy wasn't "essential" you couldn't do anything at all because the private system can't do most them either. Both of my parents are nurses & according to them at one point their hospitals were almost entirely empty, but because of that arbitrary you still couldn't access most non-urgent care which was very frustrating for them.