No, but it does bring flexibility, including services that the public system won't provide or won't provide soon enough. How long are the waitlists for hip and knee surgeries in your province? Private surgeries could shorten that list and let people who can't afford it move further up.
Let me answer your question with a question. Why do people have private health insurance? Should we make it illegal? What would making it illegal do to the public system?
I'm not saying don't properly fund the public system. It's not either or. It's and. You're stuck on either or because the US is right there. The UK does and. Norway does and. Germany does and. Australia does and. Canada and the US do or, and you know what the results are.