Should the NHS make toilet paper?
Or manufacture medical instruments?
This "NHS must not buy anything from the private sector" attitude appears to ignore reality completely.
There are many private hospitals that specialise in particular types of treatment. They don't do anything else at all so they're really quite good at it.
One of the reasons those places can specialise is because the NHS does the general care, so they don't have to.
Would you really want the NHS to refuse to send you to the best place for your replacement knee because it happened to be a private hospital?