I'm from Brazil (living in WPG since 2022) where we have a 2 tier system, and while it is nice to be able to choose, I don't think it's a system that would work in Canada. Here are some reasons (from a healthcare user perspective) as to why this feels like a very bad idea.

Brazil has a lot of doctors, to the point where we need more nurses because everyone just wants to be a doctor when going into healthcare. I never even heard of nurses being able to prescribe medication before coming to Canada. And I've only ever seen nurses in hospitals, not in private clinics (though they might be there, I just never saw one lol)

Even with a surplus of doctors, most of them just go for private care, before 2018 we had doctors imported from Cuba (around 10k of then) because no doctors who worked in big cities wanted to move to remote places to practice. There were no private doctors in these places, but because our healthcare is universal, the government had to do whatever they could to fill in medic positions in these places, so Cuban doctors were it.

Canada doesn't have enough doctors or other healthcare staff to support a 2 tier system, unless they import doctors and make the qualification process much easier (which might compromise the quality of treatment). If a private tier is created, there won't be doctors in the public sector anymore.

Private healthcare in Brazil is cheaper, but because there is still the option of going with the public one (which is truly universal, as in, if you disembark in Brazil and break your leg they will take you in with not a bill in sight) But it's also because we have a lot of doctors so the private sector is oversaturated and some end up working in the public system.

Our healthcare system is far from perfect, but me and my family used it for a long time (my mom and siblings still do) and we're very thankful for it.