Healthcare in Canada has many problems but being "public" is not the cause of them. For decades conservative governments have underfunded the medical institutions in my municipality as a way of making true on their promise of lower taxes. Now the hospitals here are understaffed for the wave of infections every year and the staff is overworked. Things could be better if people stopped chasing lower taxes every election and actually thought about where that saved money was going to go. It doesn't need to go private. Although the Ford government in Ontario seems set to lead the province in that direction by continuing the legacy of conservative governments.
Canada isn't the united states, hyperpartisan "conservative governments" nonsense is just ignorant. Our political parties are exactly the same, both support our third world healthcare system as is because it favors entrenched interests and it's politically popular. But don't let that get in the way of playing American and blaming "conservatives".
"both parties are same" is either an incredibly disingenuous interpretation or ignorance, and I can't tell which. Yes, they both ostensibly support the healthcare system in that the CPC doesn't want to say that they want to get rid of it, but you just have to look at the provincial parties recent actions to disprove the "sameness". I even gave you an example. Things don't need to be stretched at much as in the US for the two parties to employ different strategies towards healthcare.
Also I don't think you know the definition of "third word".