Fair enough, though I don’t think the difference between the Canadian single payer model and the UK model is a distinction without a difference. Lumping all systems that technically meet the definition of single payer together and concluding that “by and large, the case against single payer is the same regardless of the system” is like alleging that all multipayer systems (universal or not) suffer equally from the same problems. Any system must be regulated by the state if it is going to achieve true universality (i.e. coverage mandates, price controls, 100% public participation, etc.).
I am willing to concede that the UK is technically single payer, though I don’t think it is what most Canadians, or even most Americans, think of when they hear terms like “single payer” or “Medicare for all”. I think to the extent they do think of the UK model they are really thinking of what is better described as a single provider model, or single payer/provider model if you prefer. The NHS is an example of single ownership. The state owns and operates (as opposed to regulates) the hospitals, clinics, etc. The state is both the sole (or primary) insurer and the sole provider as opposed to the sole insurer alone as in Canada’s case. There are regions in the US where there is also a single provider, which is also often conveniently owned by the only insurance company providing coverage in that area. I suppose technically these cases represent a “single payer system” as well, at least for many of the area’s residents, yet you and I both know they aren’t what either Bernie Sanders or Paul Ryan are thinking of when they talk about single payer healthcare.
Hospitals and clinics in the UK have no means that I’m aware of to garner additional community support like they do in Canada. Nor can they easily (if at all) independently lobby either provincial or federal lawmakers for additional revenue. While the payer (insurer) is the province in Canada, funds actually come from both the provincial and federal government and in many cases funding can be and is further supplemented through private donations to independently run non-profit providers operating in a given area. Except for the federal funds part, I don’t think any of that is really true in the UK. In other words, the phrase “single payer” means exactly what it says in Canada: one primary insurance provider that pays for all basic care offered by providers within each province. For most of the population, it does not also mean a single healthcare provider and in just about every case the provider and the payer are separate entities regardless. Doctors remain in private practice and hospitals remain independently run. I think that difference can matter a great deal.