Back in the day there was a professional body and a professional qualification for Health Service Administrators as they were called then, and you wouldn't progress far up the management ladder within the NHS without completing the diploma and being registered with the Institute of Health Service Adminstrators.
Health Service Management was considered to be a specialism in its own right and there was once a national graduate training scheme for health service administrators well as schemes run at regional and local levels.
Reorganisation after reorganisation and advances in health care have resulted in a very different health service to what it once was, but hospitals are still hospitals and it’s not unreasonable to question whether doctors, nurses etc have the right expertise to manage such complex organisations and their diverse range of staff. The awful events at Chester would seem to indicate that they don’t.