I'm still waiting a "DUTCH ROLL" SOP to apply in case of degenerating yaw damper failure,
You might want to Google KC-135 Kyrgyzstan and see that the Air Force also has a problem with over reliance on automation. Due to flight control problems the aircraft developed Dutch Roll and it broke up in flight. The report suggested that the crew might have been able to recover the aircraft if they had taken manual control but they instead had attempted to engage the autopilot.
So its not just a civilian problem. It has a lot to do with reducing training to the absolute minimum and hoping that the only non-normals experienced by a crew fit neatly into the QRH and ECAM/EICAS.