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Many plants actually do rotate throughout the day to face the sun.

No, he explains that at the end. I can try to reformulate it. Imagine that you can find the orientation which gives you the maximum amount of power for a day, say E_max. If you have N panels, the total energy produced at the end of the day will be NE_max. If instead, you decide to put each panel in a specific direction, they will all produce energy E_i < E_max at the end of the day. So the total energy produce will be E_1 + E_2 + ... + E_N < NE_max.

The flat array is the more efficient design.

that assumes the power of the sun absorbed by the panel has a linear relationship to the angle to the panel, or some similar assumption. It may not be the case

Trees have leaves on all sides so that catch the sun throughout the day.

that is the point, trees don't have a flat array that doesn't move.