I don't agree with your conclusion, but that was a pretty tightly-written post. 👍 You stop just short of presenting single-payer vs. the US system as the only options. I think most people reading this would walk right through the door on that one.
No, I really don't think it's necessarily single-payer vs US system, which is why I say it's "a complicated issue".
My only significant personal experience of Canadian healthcare was hernia surgery at the Shouldice Clinic in Toronto.
"While private hospitals are not allowed under Ontario's Private Hospitals Act, Shouldice is one of seven private hospitals in the province grandfathered under the Act. The hospital has been continuously family run from its inception, but is partially publicly funded". (Interestingly, a recent patient at the Shouldice was Rand Paul who selected the Shouldice for his own hernia operation).
The treatment my mother in law received over the years from the Ontario health system seemed caring & attentive. When her cancer doctors discovered she had a brain tumour (after her previous cancers had left her in a very compromised condition), they were still ready to start further treatment even though the prospects for a successful outcome were slim to none (no death panel).
In the UK, my mother had private medical insurance & was treated for cancer at a state-of-the-art private clinic on Harley St. In the end, the treatment probably helped prolong her life by a year or so. Once the prognosis was hopeless, she went on to receive exemplary palliative care from the local NHS care providers.
My youngest daughter has had a mysterious inner ear problem that has proved very challenging to diagnose & treat. Negotiating the Ontario health system for a problem like that has not been easy - I can't imagine anyone in Canada successfully coping with something like that without the intellectual capacity & dogged persistence brought to bear by my wife. We finally received an appointment for an MRI in August. Before that, we considered taking her to a clinic in the US. Fortunately, that date has just been moved up to mid-March, so that won't now be a consideration.
It's possible to have very good people working in both public & private health care, but the bureaucracy involved in the US system actually seems to be worse in many ways than in single payer systems. Overall, the US healthcare system, as determined in a 2017 survey of the healthcare systems of 11 developed countries found the US healthcare system to be the most expensive and worst-performing in terms of health access, efficiency, and equity. In a 2018 study, the USA ranked 29th in healthcare access and quality. Of course "access" & "equity" are part of that evaluation.
Whatever your personal philosophical views on this, the reality is that access to (more or less) universal healthcare is accepted as a human right in the entire developed world outside the US. I suspect, as time goes by, Americans will increasingly come to recognize the shortcomings of the present US system & move towards a single-payer system, although I would be surprised to see the private option disappear completely.