Sure, a lot of willpower is required to hike a trail hundreds or thousands of miles long. But LESS willpower is required if you’re not carrying an anvil on your back! 
I haven’t seen statistics of the kind you’re looking for. They’re not in Mueser’s wonderful book, unfortunately-- I just checked. He does say that whether you carry 30, 40, 50, or 60 pounds doesn’t seem to have a statistically significant impact on your hiking speed. However, hikers carrying below 30 pounds do move noticably faster. The big caveat is that his data is all from people who COMPLETED the trail.
Generally, statistics about AT hikers are pretty scarce, I think. I think the rangers at Katahdin keep a pretty good record of completions, and most hikers stop by Harper’s Ferry for a picture, but that’s about it. The hordes that start at Springer each year are nameless and uncounted, so far as I know.
The impact of reducing pack weight is probably more clear on the PCT than the AT. At least anecdotally, Jardine’s popularization of lightweight hiking in the early 90’s increased completion rates dramatically.
Eric