As YOU have identified, the basis on which Scotland’s NHS is funded would be undermined if in England the UK Government decided to move to a private health insurance system for medical care.
Barnett, the UK-controlled funding formula by which the revenue of the Scottish Government is determined, relates Scottish revenue to English public expenditure.
A move from public to private insurance funding in England would cause an immense reduction in the revenue available to Scotland. It is hard to see a Scottish Government being able to maintain public funding of the NHS in the circumstances.
Given the increasing divergence in the approach of Scotland and England on the NHS, such an event seems quite possible. While Scotland will, under the Scotland Act 2012, have some additional power over income tax, if the Scottish Government were to make up the funding gap through use of this power, it’s likely there would be a substantial (probably unacceptable) shift in the tax burden to personal taxation.
The only sensible way to ensure Scotland is genuinely able to take its own decisions on the NHS funding is for Scotland to have control over taxation in Scotland generally.