I would imagine the vast majority of CFIT is when the pilot cannot see the terrain... hence it's "controlled flight"... even in the model example, you have the luxury of being able to see the wall..
How to avoid CFIT? Avoid the situation that causes it... if vfr to imc, then turn arround. if ifr in imc, plan well.
If there's heavy fog on the motorway, do we still drive normally because we know how to do an emergency stop, or do we put a fog light on and slow down to avoid having to even need an emergency manoeuvre ?