You mistake the forces at work.
You see, the forces at work are not the wind perse, rather wind is the catalyst for attracting the true force at work, the atmosphere.
On one side, the air passes a flat smooth side, and on the other it passes over a large curve. When air passes over a curved shape, such as a turbine blade, you create a pressure differential. Faster air, lower pressure.
The atmosphere then sees this lower pressure area around the blade and says “absolutely fucking not” and slams the surrounding air towards it.
If the blades were any wider, the drag from the surrounding air would negate the atmospheric force significantly. So thin it is.
Put three blades at 120° on an axis and you have a wind turbine.
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