Everyone acknowledges in principle that automation dependency is a bad thing, but almost all of my captains look at me funny when I ask to handfly all the way to altitude. The senior is instructor also pushes automation very hard.
+1 for learning to trim. That is indeed key, and very few of aforementioned captains ever touch it.
Re automation making the industry safer, that is true to a point, but still the problem of dependency remains. Also, a lot of the improvement in the accident rate is down to such things as EGPWS, TCAS, and precision approaches, rather than autopilots.
I was lucky. I never even saw a FD or had a functional, approach capable AP until I had 8000 hrs.