Agree with some of what you say. Good administrators are worth their weight, not only do they do their jobs well (freeing the nurses / doctors up to do their thing) but they also look for process improvement. Bad administrators do nothing of the latter. The NHS seems to have a lot of the latter. When I was in the UK, nurses that I knew, would reminisce about the old days of the ward sister and how much better wards were run.
I'm also going through some hand therapy at the moment. My doctor is scottish and we were talking about the UK vs Australian system, and he mentioned that he loves the Aussie system, he could directly refer me to a hand therapist, whereas in the UK they would have to refer you to a hand surgeon (even when they don't believe surgery is necessary), who would then refer you to a hand therapist (a waste of the surgeons time). Once you factor this through for many different referrals there would be a heap of time wasted within the entire NHS system.
The NHS system is good, but I much prefer the Aussie model. It seems to have got the balance between public and private servicing and how they setup process flowthrough of the system seems to be far better than the almost pure public system in the UK (I know they have private but its only used by the rich).