The problem is the managing of the automation...
Exactly. In simulator training, many times I've seen the automation, doing exactly what the crew tells it to do, fly a perfectly serviceable helicopter into the ground whilst the crew watched. When crews are doing "stick and rudder" hand flying, the prevalence of CFIT, in my experience, seems to be far less. The physical interaction of the stick and rudder flying seems to install an additional degree of mental alertness that you just don't see to the same extent when pilots are just monitoring automation. As a teacher it can get frustrating to watch, you feel like ripping out all the automation and have the crews get back to fundamentals and using just the basic set of IFR tools.