Indelible in my mind is reading the accident report CVR where a Boeing 737 took off at night somewhere in the Middle East and the captain asked his first officer to engage the autopilot. I think the F/O replied along the lines "God Willing - autopilot engaged" But he had not engaged the autopilot because the captain still had pressure on the control wheel preventing the AP from engaging. All the F/O was apparently doing was reading back the captain's command to engage the AP.
Eventually the 737 wandered around the night sky in ever increasing angles of bank until it was in a seriously unusual attitude because no one was flying it. The absolutely horrifying part then started as the aircraft went into a steep spiral with the captain shouting desperately "Engage the Auto-pilot - engage the autopilot! Then oblivion...
That particular event and there are many others similar, if one cares to trawl through ICAO accident reports involving loss of control in IMC and that includes more recently, straight forward low altitude go arounds in IMC, demonstrates a fundamental flaw in recurrent simulator training starting from the first type rating.
That flaw is so easily fixed by company initiative in designing the simulator training syllabus to accent manual flying skills instead of button pressing ad nauseum. If the crew lack the ability to seamlessly switch from autopilot controlled flight to manually controlled flight without drama, then again this reflects adversely on their training in the simulator. I am sure every airline management work on the theory that accidents only happen to other operators so no need to worry about simulator training beyond regulatory box ticking.
As one Boeing Seattle 787 test pilot told a Boeing 787 simulator instructor "We designed the 787 around the basis it will be flown by incompetent pilots." What an indictment on the quality of some airline crews flying jet transports.