A GPS is superior in many ways to a compass. It is very hard to locate yourself with accuracy on a map on a clear day let alone under conditions where you cannot see or identify the surrounding peaks. I have triangulated myself using a geologist compass and protractors and even with perfect conditions it was still hard to place myself on a map. With a GPS I would be able to place myself perfectly even if there was fog or trees to block my view.
On the PCT I didn't have or know how to use a GPS and most of the time I never bothered with my compass. Instead I relied on my watch. After a few weeks I knew what my average pace was. With the data book and guide book and my watch, I could pass a point of interest, check the time, check for the distance to the next point of interest in the book and then calculate the time it would take to get there. At the appointed time, I could look around me for the point of interest. I could be within 5 minutes accuracy on a regular basis this way. I came to rely upon this means of navigation almost entirely.
By looking around, I mean really looking. I met a many people who missed things because they didn't look. I would find sticks that perhaps had once been aligned as arrows but now were scattered, very faint tracks in the dirt, signs facing the wrong way on trees that had fallen over, rocks that appeared out of place to me. With my watch, I'd know it was time to start looking and I'd look very carefully.
I am reminded of the book Clan of the Cave Bear. It's fiction, but I always remember how in this book when the people needed a map, it would not be a diagram of a bird's eye view of the land but of the points of interest you'd see as you went along. I read the book a long time ago and thought if this really was how things had been done at any time in our human history, it certainly makes a lot of sense to me because it is how I make sense of my landscape on a daily basis all the time. I am also reminded of the trees they have found throughout the eastern US that had once been purposefully bent so that they would form a directional pointer to the way to go to get somewhere.
Navigating by such ground-level means has been with us a long time. They are good skills to have and seem to be dying as much as compass-reading due to our overly distracted, non-introspective, non-observant culture.