In the real world, large chunks of the NHS are already sort-of privatised. In Gloucester, many cataract operations are carried out by a private company; which, yes, has cut waiting times considerably. In Oxford, three GP practices are now owned by a private company. And pensioners and leavers con join NHS Professionals, another limited company, and work when they want and where they want, often with better pay and definitely with less hassle. In all cases, who knows, Trump Industries Inc might do a better job. Doubt it, though.
Years ago when I worked in Greece, families used to fly their poorly relatives to London to get better medical treatment. Now it’s cheaper, even with the cost of flights and hotels, to go to Lithuania for a hip replacement and Hungary or Turkey for a bit of dental work.