The ultimate example that peripheral vision and looking far down is essential to good landings I learned when I was trying to fly helicopters. To learn to hover is the skill that needs mastering before anything much can be done in a helicopter, so normally that comes pretty early in training (although I never finished my training). As so many before me, I struggled to get it right. I was looking out the side or bottom windows of the Hughes 300C and by the time it came to correct, it was almost always too late and the oscillations got worse and worse until my instructor had to save the day. Over-corrected mess in conjunction with being late on the ball. This went on for some time. Finally my instructor said:
"See that house far away at the edge of the field?"
"Yes?"
"Fixate on that and try to hover"
"OK..."
And that was literally it. I could immediately hover ten seconds later. It's like that moment when you learn to ride a bike - it just clicks.
Although hovering and landing in a FW are not the same, they use the same skill sets and visual signals. Also, helicopter long-lining with underslung loads uses these skills to not only judge hover, but also height very precisely. Looking straight down at the target one wouldn't think that enough visual cues can be provided, but the peripheral vision makes this possible. Here's a little film made by veteran helicopter pilot Earl Watters as he lifts a plane wreckage out of the desert. You can see that he looks straight down for all lifting operations, and still manages to judge height and hover very precisely at 1:33: