And I am (still) baffled that the starting viewpoint from the American side is that with single payer health care private insurance would be 'abolished' or otherwise become unavailable and/or illegal. Huh? Of course not. It's simply a base level of care given to everyone. If you have the money and desire then why wouldn't you pay for private insurance, or cash out of pocket for a private hospital?
And better yet, that private insurance will become cheaper: it can exclude the rare, chronic and expensive diseases you probably won't get. (As if you ever do, you could rely on the base single payer coverage.)