There are three main reasons for a/c accidents:
(1) The pilot: Prime suspect, if only for the reason that he/she was the last to touch the a/c.
(2) Mechanical failure: Increasingly rare these days thanks to better design and testing of materials.
(3) Systems failures: Unfortunately creeping up the league table.
I admit I am not a jet jockey, but I have found myself in turbulent air in IMC. Before the a/p tripped I would take control (it was a crude a/p system), the reason; not many recover from unusual attitudes in actual turbulence, much better to take control of a stable aircraft and fly attitude/power.
With advanced systems, the a/p can probably fly the aircraft better than the crew, certainly more economically. When things start to go south, however, the system compensates with its built in redundancy (therein lies the danger). When it finally gives up, it hands over a, probably, uncontrollable aircraft to an inexperienced crew. I do not mean to be derogatory with the term inexperienced, my good buddy is a TC on 777s and I have nothing but admiration for his skills; but I would not class myself an experienced aviator if I switched in the a/p 12 secs after take off and off after landing.
Remember that when you do your sim/flight training you're geared up ready for what is about to come your way; much different to being in the cruise at FL350 on a dark night in the middle of nowhere.
Training has got to start including, recovery after major systems failure or better still recognizing the onset of a systems failure and stopping it becoming another AF.
I'm not optimistic that that can be achieved, humans are not good at monitoring computers; much better the other way around.