I am assuming (sorry if wrong) that you are talking about the NHS Trusts when talking about disciplinary/sacking within the NHS. My husband works in the NHS (not the trusts) in HR having worked for years in the private sector. Where he is, the managers don't have a clue how to manage their staff and the majority are too scared to deal with problem staff. Consequently some staff have been getting away with all sorts including bullying. This is now slowly being dealt with. He is amazed that apparently staff can't be suspended even if accusations of bullying are being looked into. This obviously leaves the accuser open to intimidation. This would never happen in the private sector where generally action is taken a lot more swiftly and I would add still within employment law. As I say this is not about the NHS trusts as I've no idea how well they are managed.
That's bonkers, if not against employment law, and not something I've ever known during my 30 odd years in the Health Service. I did return from my honeymoon many years ago to discover I was being suspended as I'd been accused of rape during my absence. As the reported act happened while I was actually still in the Canaries I suggested I could return to work or I'd be stood outside the hospital with a large sign and the local press next day. I returned to work. That maybe was me bullying a bit but I was jolly upset and a jobsworth was being very silly, and nasty.
As I hinted it's pretty easy to pick out examples of bad practices from public and private sectors. But even a smug bugger like myself should try not to generalise too much or swallow wholesale some of the convenient myths. I think overall small employers (which by default are mainly private) can intimidate and dismiss staff the easier, however there remain institutional cultures in the public sector which are far from healthy. To me it just feels the constant drip drip of negatives will hardly help recruitment of staff in roles we keep saying are important, but maybe that's the point.

