American here. This is a bad line of argument. Americans only get 1 insurer at a time, so comparing the NHS to the union of all possible insurers is a strawman argument. Each single insurer covers roughly the same procedures that the NHS does (although insurers frequently deny legit claims and will deny all claims past a certain annual/lifetime claims limit).

And your example is at a single point in time. At one point in time, no US insurer covered that procedure (before it was standardized) and eventually if it actually does affordably improve outcomes, it will be covered by NHS.

For me, the most valuable feature of CA's system is that its incentives are at least mostly aligned with your long term health interests. Only HMOs and active duty soldiers (covering maybe 15% of Americans at most) in the USA are mostly aligned this way. The remainder of US health care is minimally aligned, so costs are outrageous and long term outcomes are sometimes good, but sometimes terrible.

The private insurer is 2x the cost. You don't think people travel outside the US to receive care? Medical tourism is alive and well in the US due to the cost burdens for-profit healthcare requires.