I would dispute that there are staffing issues in the NHS as a result of poor management (I would say that as a retired NHS manager!).
I feel that there are fundamental issues with the NHS that can't be solved *purely* by throwing money at it.
I support the long term view that prevention of ill health and having a healthy population is uppermost - but that has to be a 20 year plan.
But today - the NHS has become all things to all people with little focus on doing anything excellently. Mental health care, emergency services, and primary care are all beyond creaking at the seams.
I think in the short term the use of the private sector can't be avoided. The financial rules around procurement & disposal of capital equipment are looser in the private sector but the sector is parasitical on NHS training & expertise.
If parts of the NHS were ultimately given more financial freedo, reliance on private providers could be reduced.