> And, as pointed out, people additionally have the option of taking out additional coverage,
That's like saying "people additionally have the option of paying out-of-pocket". Remember, by definition, the expected monetary value of insurance is negative, so unless the private insurance is being subsidized by taxpayer dollars (defeating the whole point), this is equivalent to saying that people are still free to pay for treatments themselves.
> NICE's recommendations are not subject to the NHS budget. They are independent for a reason. Cost efficiency of a treatment enters into their assessments, but they do not have final say on which treatments are offered. They make recommendations based on the clinical need and document efficacy, outcomes and costs. It's up to the NHS to then allocate funds accordingly.
You can't escape the fact that, at the end of the day, the process still amounts to the same thing. Given a finite budget, decisions are made on how to allocate that funding based on clinical data, resulting in some people not receiving treatment, even though they would otherwise benefit clinically from it. What the NHS does is not fundamentally different from what insurance companies do.
Saying that it's subject to "democratic control" doesn't really mean a whole lot, except that the process ends up being a lot slower, and it becomes a political battle. (Notice that PrEP has been available in the US for five years at zero cost to patients, and it's still not available in the UK. Or, notice that the cure for HCV is generally accessible on private insurance in the US, but almost nobody in the UK is able to receive it through the NHS.)