I'm not sure how much of this the kid actually discovered on his own. The Wikipedia page on Phyllotaxis cites plenty of past research on why the Fibonacci sequence shows up (and the kid oddly hand copied the illustrations from that page).
It's an emergent pattern from the branches shoving each other around as they grow. It minimizes the overlap of the leaves if they are being added indefinitely. If you know in advance how many leaves/panels there will be then obviously you can just space them evenly. If you ran that experiment with one tree of evenly spaced/angled panels and one tree of golden angle spaced panels, I think the evenly spaced one would win.
Crucial difference: the tree-leaf problem is about how to arrange leaves which are shading each other; but here he compares such a "tree" with a flat array that has no overlaps at all. He claims that the tree generates more energy than the no-overlaps array, which is impossible. I have a longer comment about this in the other thread:
I think it is also related to the angle of sunlight falling on the leaves - not just the shading. The passive arrays may be completely unshaded but they may not receive the optimum sunlight through out the day.
It's not impossible, because the sun's relative position changes, and the closer to orthogonal the light, the better the efficiency of the solar cell. By taking optimal advantage of the height, this design is closer to orthogonality more of the time, and is thus more efficient per ground area (though not per solar cell area, as you demonstrate).
Now, if your solar array were mounted such that it actively maintained orthogonality to the sun (heliotropism), I expect you'd do even better, but that kind of active system is more subject to failure.
It's an emergent pattern from the branches shoving each other around as they grow. It minimizes the overlap of the leaves if they are being added indefinitely. If you know in advance how many leaves/panels there will be then obviously you can just space them evenly. If you ran that experiment with one tree of evenly spaced/angled panels and one tree of golden angle spaced panels, I think the evenly spaced one would win.