I think accident rates could be reduced if a greater proportion of initial and recurrent training involved dealing with issues that are actually causing most of the accidents. Someone with more spare time than me might do some research and summarise what these are, but training in poor visibility conditions, with aircraft near MTOW, high winds, difficult approaches, distracting cockpit environments, spurious distracting warnings, etc etc, would all be very useful in highlighting weaknesses for pilots and generating both more competence and more respect for the hazards of such things. I've long thought that too much training focus is often on dealing with mechanical emergencies - which very rarely occur. The vast majority of accidents involve perfectly serviceable aircraft.
Of course it's important (and not easy) to do this without adding significant risk getting involved in risky procedures, as with S/E EOLs. Just how competent the trainers are is also a significant issue - sometimes instructors have inadequate experience themselves of real world operational risks.
Pittsextra - you quite reasonably attach great importance to AAIB accident reports, but I am not sure how much help it would really be if they were produced in even half the time. Accuracy is critical. I think most of the time the basic causes of accidents are fairly obvious and indeed with regard to what can be learnt to avoid future acidents, often covered in a small range of hypotheses here on Pprune! If we consider a few examples, the Haughey 139 was almost certainly pilot disorentation manually flying in IMC, Kent S76similar, Sumburgh Super Puma probably dozy monitoring of an IMC approach, Glasgow 135 probably poor fuel managment, though less certain admittedly -I'm sure 135 pilots are more careful on transfer pump use now though.
Of course there are occasions where particularly say mechanical failure - and I think you're pretty hot on this, eg ? AS332 MGBX - are identifed and rapid industry awareness vital. There again, I suspect that even if the AAIB report isn't out, between the CAA and manufacturers preventative management is usually well underway.
Most importantly though as pilots we've got to take responsibility for our own actions - usually, but certainly not always, accidents are fundamentally our fault, not that of the "system". And let's not forget that the "system" ultimately relies on judgements of individuals - like pilots - and buck passing should be avoided. As helicopter pilots we enjoy greater freedom of making our own judgements, but with that comes more responsibility.