I would say that the first government to suggest ending treatment free at the point of delivery would face massive opposition from across the political spectrum.
Private companies are quite capable of delivering all kinds of services at good value and still make a profit. There is absolutely no reason why private companies should be excluded from NHS work on dogmatic grounds. Obviously some companies are better than others and contracts need careful management, but there is also exceedingly bad practice within the NHS itself that needs 'weeding out'.
A few years ago a friend of mine did some part-time work at the local hospital to top-up his pension. Having run his own company in the past he was appalled by what he saw. Operations were being cancelled because no one had autoclaved the instruments or cleaned the theatres properly!
Let's look at education...the model for everything these days.
Overriding everything at the moment is the fact that there is a teacher shortage in a sector which has little or no incentive for people to come into it. A quarter of those trained do not stay in the profession for more than a few years. It is a sector where experience does not count due to government regularly ripping up the rule book and making it very easy to get rid of Old dogs who can't or refuse to learn new tricks.
Worse is internal competition between LEA and academy chains and between academy chains, a post code lottery in education and after 25 years of a sacred inspection system failure is still or more rife than in 1990.
Academy chains are becoming more like local authorities but without the ability for joined up planning with other services making a mockery of local management.
The big problem is that it has the worst of all worlds.
The unneccesity of contracting out.
Public servants giving out money to private contractors.
Your dilemma is this. If public servants cannot doctrinally be trusted to manage services why can they be trusted to contract them out?
It seems to me that private health had it's shout last century up to 1945 and never made a very good fist of it. Why should it work now?