As a Canadian, I would caution against the kind of universal health plan we have. But yes I agree there should be some kind of public healthcare. Perhaps more as a government owned hospitals and clinics alongside the private ones rather than the fully public system we have here which comes with its own host of problems.
I think it's easy to shout free healthcare as a slogan but I think the important bit is how it's implemented.
I don't think anyone really envies the American system. We have all the capacity problems that you guys do up north, and we pay a lot more out of our own pockets for the pleasure. Our results are also worse.
I don't think anyone from any country thinks their healthcare system is perfect or even sufficient. It all kind of stinks although some countries it is easier to solve problems with above average money (but not if you are average). We need to fundamentally figure out how to do more with less, automation (AI) could help out a lot here and I don't care about purists who want hand crafted artisanal advice about how they need to lose weight or they will die of a heart attack. But otherwise, a lot of problems exist just due to bad incentives.
I'm curious how Taiwan operates. It's a public side insurance system with mostly (if not all private hospitals). Obviously very different population case though, much smaller island.