I'm more familiar with the Spanish, Irish and UK systems. I tried to find a nice document giving numbers for what I was describing, but most of what I can find is anecdotal, and the official reports are weren't quantitative.
Here's an article from an Irish newspaper last year that gives a rough guess (though of course there are other factors): https://www.irishtimes.com/news/health/are-patient-waiting-l...
I'm certainly open to US insurance companies paying me to shill on hn against Canadian healthcare, but right now I'm only saying these things out of the goodness of my heart.
And no, I don't see a direct link between public health care and wait times. The German issues are mostly caused by a bloated bureaucracy.
I also think that these (some several year) wait times aren't unavoidable. Management of these national public health systems is fabulously complicated and difficult and expensive, but it could certainly be done much better. In the end I think a country that really wanted to, and was willing to pay, could have a public system at least as good as what a 1%er in the US gets.
Theoretically I could switch to Germany's private insurance scheme. I have no willingness to do so.
I don't know of any public health care system in developed countries that have really these issues. I do know so, that a lot of that comes from a PR campaign run by US insurances against the Canadian system.